diff --git a/python/plugins/processing/tests/testdata/expected/concave_hull_points_03_geos.gml b/python/plugins/processing/tests/testdata/expected/concave_hull_points_03_geos.gml
new file mode 100644
index 00000000000..70d0ea51626
--- /dev/null
+++ b/python/plugins/processing/tests/testdata/expected/concave_hull_points_03_geos.gml
@@ -0,0 +1,16 @@
+<?xml version="1.0" encoding="utf-8" ?>
+<ogr:FeatureCollection
+     gml:id="aFeatureCollection"
+     xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
+     xsi:schemaLocation="http://ogr.maptools.org/ concave_hull_points_03_geos.xsd"
+     xmlns:ogr="http://ogr.maptools.org/"
+     xmlns:gml="http://www.opengis.net/gml/3.2">
+  <gml:boundedBy><gml:Envelope srsName="urn:ogc:def:crs:EPSG::4326"><gml:lowerCorner>-5 0</gml:lowerCorner><gml:upperCorner>3 8</gml:upperCorner></gml:Envelope></gml:boundedBy>
+                                                                                                                                                                             
+  <ogr:featureMember>
+    <ogr:concave_hull_points_03_geos gml:id="concave_hull_points_03_geos.0">
+      <gml:boundedBy><gml:Envelope srsName="urn:ogc:def:crs:EPSG::4326"><gml:lowerCorner>-5 0</gml:lowerCorner><gml:upperCorner>3 8</gml:upperCorner></gml:Envelope></gml:boundedBy>
+      <ogr:geometryProperty><gml:Polygon srsName="urn:ogc:def:crs:EPSG::4326" gml:id="concave_hull_points_03_geos.geom.0"><gml:exterior><gml:LinearRing><gml:posList>-5 0 -1 0 1 1 2 2 3 3 2 5 -1 8 -1 7 1 4 -5 0</gml:posList></gml:LinearRing></gml:exterior></gml:Polygon></ogr:geometryProperty>
+    </ogr:concave_hull_points_03_geos>
+  </ogr:featureMember>
+</ogr:FeatureCollection>
diff --git a/python/plugins/processing/tests/testdata/expected/concave_hull_points_03.xsd b/python/plugins/processing/tests/testdata/expected/concave_hull_points_03_geos.xsd
similarity index 91%
rename from python/plugins/processing/tests/testdata/expected/concave_hull_points_03.xsd
rename to python/plugins/processing/tests/testdata/expected/concave_hull_points_03_geos.xsd
index 754d43b6a49..d1c4e19f5cc 100644
--- a/python/plugins/processing/tests/testdata/expected/concave_hull_points_03.xsd
+++ b/python/plugins/processing/tests/testdata/expected/concave_hull_points_03_geos.xsd
@@ -34,8 +34,8 @@
     </xs:extension>
   </xs:complexContent>
 </xs:complexType>
-<xs:element name="concave_hull_points_03" type="ogr:concave_hull_points_03_Type" substitutionGroup="gml:AbstractFeature"/>
-<xs:complexType name="concave_hull_points_03_Type">
+<xs:element name="concave_hull_points_03_geos" type="ogr:concave_hull_points_03_geos_Type" substitutionGroup="gml:AbstractFeature"/>
+<xs:complexType name="concave_hull_points_03_geos_Type">
   <xs:complexContent>
     <xs:extension base="gml:AbstractFeatureType">
       <xs:sequence>
diff --git a/python/plugins/processing/tests/testdata/expected/concave_hull_points_03.gml b/python/plugins/processing/tests/testdata/expected/concave_hull_points_03_qgis.gml
similarity index 74%
rename from python/plugins/processing/tests/testdata/expected/concave_hull_points_03.gml
rename to python/plugins/processing/tests/testdata/expected/concave_hull_points_03_qgis.gml
index 4aca65ec5a6..483f2353a34 100644
--- a/python/plugins/processing/tests/testdata/expected/concave_hull_points_03.gml
+++ b/python/plugins/processing/tests/testdata/expected/concave_hull_points_03_qgis.gml
@@ -2,15 +2,15 @@
 <ogr:FeatureCollection
      gml:id="aFeatureCollection"
      xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
-     xsi:schemaLocation="http://ogr.maptools.org/ concave_hull_points_03.xsd"
+     xsi:schemaLocation="http://ogr.maptools.org/ concave_hull_points_03_qgis.xsd"
      xmlns:ogr="http://ogr.maptools.org/"
      xmlns:gml="http://www.opengis.net/gml/3.2">
   <gml:boundedBy><gml:Envelope srsName="urn:ogc:def:crs:EPSG::4326"><gml:lowerCorner>1 2</gml:lowerCorner><gml:upperCorner>3 5</gml:upperCorner></gml:Envelope></gml:boundedBy>
                                                                                                                                                                               
   <ogr:featureMember>
-    <ogr:concave_hull_points_03 gml:id="concave_hull_points_03.0">
+    <ogr:concave_hull_points_03_qgis gml:id="concave_hull_points_03_qgis.0">
       <gml:boundedBy><gml:Envelope srsName="urn:ogc:def:crs:EPSG::4326"><gml:lowerCorner>1 2</gml:lowerCorner><gml:upperCorner>3 5</gml:upperCorner></gml:Envelope></gml:boundedBy>
-      <ogr:geometryProperty><gml:Polygon srsName="urn:ogc:def:crs:EPSG::4326" gml:id="concave_hull_points_03.geom.0"><gml:exterior><gml:LinearRing><gml:posList>2 2 3 3 2 5 1 4 2 2</gml:posList></gml:LinearRing></gml:exterior></gml:Polygon></ogr:geometryProperty>
-    </ogr:concave_hull_points_03>
+      <ogr:geometryProperty><gml:Polygon srsName="urn:ogc:def:crs:EPSG::4326" gml:id="concave_hull_points_03_qgis.geom.0"><gml:exterior><gml:LinearRing><gml:posList>2 2 3 3 2 5 1 4 2 2</gml:posList></gml:LinearRing></gml:exterior></gml:Polygon></ogr:geometryProperty>
+    </ogr:concave_hull_points_03_qgis>
   </ogr:featureMember>
 </ogr:FeatureCollection>
diff --git a/python/plugins/processing/tests/testdata/expected/concave_hull_points_07.xsd b/python/plugins/processing/tests/testdata/expected/concave_hull_points_03_qgis.xsd
similarity index 91%
rename from python/plugins/processing/tests/testdata/expected/concave_hull_points_07.xsd
rename to python/plugins/processing/tests/testdata/expected/concave_hull_points_03_qgis.xsd
index 63cfb6bba92..037808e0bb9 100644
--- a/python/plugins/processing/tests/testdata/expected/concave_hull_points_07.xsd
+++ b/python/plugins/processing/tests/testdata/expected/concave_hull_points_03_qgis.xsd
@@ -34,8 +34,8 @@
     </xs:extension>
   </xs:complexContent>
 </xs:complexType>
-<xs:element name="concave_hull_points_07" type="ogr:concave_hull_points_07_Type" substitutionGroup="gml:AbstractFeature"/>
-<xs:complexType name="concave_hull_points_07_Type">
+<xs:element name="concave_hull_points_03_qgis" type="ogr:concave_hull_points_03_qgis_Type" substitutionGroup="gml:AbstractFeature"/>
+<xs:complexType name="concave_hull_points_03_qgis_Type">
   <xs:complexContent>
     <xs:extension base="gml:AbstractFeatureType">
       <xs:sequence>
diff --git a/python/plugins/processing/tests/testdata/expected/concave_hull_points_07_geos.gml b/python/plugins/processing/tests/testdata/expected/concave_hull_points_07_geos.gml
new file mode 100644
index 00000000000..868cb02e392
--- /dev/null
+++ b/python/plugins/processing/tests/testdata/expected/concave_hull_points_07_geos.gml
@@ -0,0 +1,16 @@
+<?xml version="1.0" encoding="utf-8" ?>
+<ogr:FeatureCollection
+     gml:id="aFeatureCollection"
+     xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
+     xsi:schemaLocation="http://ogr.maptools.org/ concave_hull_points_07_geos.xsd"
+     xmlns:ogr="http://ogr.maptools.org/"
+     xmlns:gml="http://www.opengis.net/gml/3.2">
+  <gml:boundedBy><gml:Envelope srsName="urn:ogc:def:crs:EPSG::4326"><gml:lowerCorner>-5 0</gml:lowerCorner><gml:upperCorner>3 8</gml:upperCorner></gml:Envelope></gml:boundedBy>
+                                                                                                                                                                             
+  <ogr:featureMember>
+    <ogr:concave_hull_points_07_geos gml:id="concave_hull_points_07_geos.0">
+      <gml:boundedBy><gml:Envelope srsName="urn:ogc:def:crs:EPSG::4326"><gml:lowerCorner>-5 0</gml:lowerCorner><gml:upperCorner>3 8</gml:upperCorner></gml:Envelope></gml:boundedBy>
+      <ogr:geometryProperty><gml:Polygon srsName="urn:ogc:def:crs:EPSG::4326" gml:id="concave_hull_points_07_geos.geom.0"><gml:exterior><gml:LinearRing><gml:posList>-5 0 -1 0 1 1 2 2 3 3 2 5 -1 8 -1 7 1 4 -5 0</gml:posList></gml:LinearRing></gml:exterior></gml:Polygon></ogr:geometryProperty>
+    </ogr:concave_hull_points_07_geos>
+  </ogr:featureMember>
+</ogr:FeatureCollection>
diff --git a/python/plugins/processing/tests/testdata/expected/concave_hull_points_07_geos.xsd b/python/plugins/processing/tests/testdata/expected/concave_hull_points_07_geos.xsd
new file mode 100644
index 00000000000..b94b03f2d93
--- /dev/null
+++ b/python/plugins/processing/tests/testdata/expected/concave_hull_points_07_geos.xsd
@@ -0,0 +1,47 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<xs:schema 
+    targetNamespace="http://ogr.maptools.org/"
+    xmlns:ogr="http://ogr.maptools.org/"
+    xmlns:xs="http://www.w3.org/2001/XMLSchema"
+    xmlns:gml="http://www.opengis.net/gml/3.2"
+    xmlns:gmlsf="http://www.opengis.net/gmlsf/2.0"
+    elementFormDefault="qualified"
+    version="1.0">
+<xs:annotation>
+  <xs:appinfo source="http://schemas.opengis.net/gmlsfProfile/2.0/gmlsfLevels.xsd">
+    <gmlsf:ComplianceLevel>0</gmlsf:ComplianceLevel>
+  </xs:appinfo>
+</xs:annotation>
+<xs:import namespace="http://www.opengis.net/gml/3.2" schemaLocation="http://schemas.opengis.net/gml/3.2.1/gml.xsd"/>
+<xs:import namespace="http://www.opengis.net/gmlsf/2.0" schemaLocation="http://schemas.opengis.net/gmlsfProfile/2.0/gmlsfLevels.xsd"/>
+<xs:element name="FeatureCollection" type="ogr:FeatureCollectionType" substitutionGroup="gml:AbstractFeature"/>
+<xs:complexType name="FeatureCollectionType">
+  <xs:complexContent>
+    <xs:extension base="gml:AbstractFeatureType">
+      <xs:sequence minOccurs="0" maxOccurs="unbounded">
+        <xs:element name="featureMember">
+          <xs:complexType>
+            <xs:complexContent>
+              <xs:extension base="gml:AbstractFeatureMemberType">
+                <xs:sequence>
+                  <xs:element ref="gml:AbstractFeature"/>
+                </xs:sequence>
+              </xs:extension>
+            </xs:complexContent>
+          </xs:complexType>
+        </xs:element>
+      </xs:sequence>
+    </xs:extension>
+  </xs:complexContent>
+</xs:complexType>
+<xs:element name="concave_hull_points_07_geos" type="ogr:concave_hull_points_07_geos_Type" substitutionGroup="gml:AbstractFeature"/>
+<xs:complexType name="concave_hull_points_07_geos_Type">
+  <xs:complexContent>
+    <xs:extension base="gml:AbstractFeatureType">
+      <xs:sequence>
+        <xs:element name="geometryProperty" type="gml:SurfacePropertyType" nillable="true" minOccurs="0" maxOccurs="1"/> <!-- restricted to Polygon --><!-- srsName="urn:ogc:def:crs:EPSG::4326" -->
+      </xs:sequence>
+    </xs:extension>
+  </xs:complexContent>
+</xs:complexType>
+</xs:schema>
diff --git a/python/plugins/processing/tests/testdata/expected/concave_hull_points_07.gml b/python/plugins/processing/tests/testdata/expected/concave_hull_points_07_qgis.gml
similarity index 73%
rename from python/plugins/processing/tests/testdata/expected/concave_hull_points_07.gml
rename to python/plugins/processing/tests/testdata/expected/concave_hull_points_07_qgis.gml
index c660eb66978..6990a79a11b 100644
--- a/python/plugins/processing/tests/testdata/expected/concave_hull_points_07.gml
+++ b/python/plugins/processing/tests/testdata/expected/concave_hull_points_07_qgis.gml
@@ -2,15 +2,15 @@
 <ogr:FeatureCollection
      gml:id="aFeatureCollection"
      xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
-     xsi:schemaLocation="http://ogr.maptools.org/ concave_hull_points_07.xsd"
+     xsi:schemaLocation="http://ogr.maptools.org/ concave_hull_points_07_qgis.xsd"
      xmlns:ogr="http://ogr.maptools.org/"
      xmlns:gml="http://www.opengis.net/gml/3.2">
   <gml:boundedBy><gml:Envelope srsName="urn:ogc:def:crs:EPSG::4326"><gml:lowerCorner>-1 0</gml:lowerCorner><gml:upperCorner>3 8</gml:upperCorner></gml:Envelope></gml:boundedBy>
                                                                                                                                                                              
   <ogr:featureMember>
-    <ogr:concave_hull_points_07 gml:id="concave_hull_points_07.0">
+    <ogr:concave_hull_points_07_qgis gml:id="concave_hull_points_07_qgis.0">
       <gml:boundedBy><gml:Envelope srsName="urn:ogc:def:crs:EPSG::4326"><gml:lowerCorner>-1 0</gml:lowerCorner><gml:upperCorner>3 8</gml:upperCorner></gml:Envelope></gml:boundedBy>
-      <ogr:geometryProperty><gml:Polygon srsName="urn:ogc:def:crs:EPSG::4326" gml:id="concave_hull_points_07.geom.0"><gml:exterior><gml:LinearRing><gml:posList>1 1 2 2 3 3 2 5 -1 8 -1 7 1 4 -1 0 1 1</gml:posList></gml:LinearRing></gml:exterior></gml:Polygon></ogr:geometryProperty>
-    </ogr:concave_hull_points_07>
+      <ogr:geometryProperty><gml:Polygon srsName="urn:ogc:def:crs:EPSG::4326" gml:id="concave_hull_points_07_qgis.geom.0"><gml:exterior><gml:LinearRing><gml:posList>1 1 2 2 3 3 2 5 -1 8 -1 7 1 4 -1 0 1 1</gml:posList></gml:LinearRing></gml:exterior></gml:Polygon></ogr:geometryProperty>
+    </ogr:concave_hull_points_07_qgis>
   </ogr:featureMember>
 </ogr:FeatureCollection>
diff --git a/python/plugins/processing/tests/testdata/expected/concave_hull_points_07_qgis.xsd b/python/plugins/processing/tests/testdata/expected/concave_hull_points_07_qgis.xsd
new file mode 100644
index 00000000000..8e295bd3007
--- /dev/null
+++ b/python/plugins/processing/tests/testdata/expected/concave_hull_points_07_qgis.xsd
@@ -0,0 +1,47 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<xs:schema 
+    targetNamespace="http://ogr.maptools.org/"
+    xmlns:ogr="http://ogr.maptools.org/"
+    xmlns:xs="http://www.w3.org/2001/XMLSchema"
+    xmlns:gml="http://www.opengis.net/gml/3.2"
+    xmlns:gmlsf="http://www.opengis.net/gmlsf/2.0"
+    elementFormDefault="qualified"
+    version="1.0">
+<xs:annotation>
+  <xs:appinfo source="http://schemas.opengis.net/gmlsfProfile/2.0/gmlsfLevels.xsd">
+    <gmlsf:ComplianceLevel>0</gmlsf:ComplianceLevel>
+  </xs:appinfo>
+</xs:annotation>
+<xs:import namespace="http://www.opengis.net/gml/3.2" schemaLocation="http://schemas.opengis.net/gml/3.2.1/gml.xsd"/>
+<xs:import namespace="http://www.opengis.net/gmlsf/2.0" schemaLocation="http://schemas.opengis.net/gmlsfProfile/2.0/gmlsfLevels.xsd"/>
+<xs:element name="FeatureCollection" type="ogr:FeatureCollectionType" substitutionGroup="gml:AbstractFeature"/>
+<xs:complexType name="FeatureCollectionType">
+  <xs:complexContent>
+    <xs:extension base="gml:AbstractFeatureType">
+      <xs:sequence minOccurs="0" maxOccurs="unbounded">
+        <xs:element name="featureMember">
+          <xs:complexType>
+            <xs:complexContent>
+              <xs:extension base="gml:AbstractFeatureMemberType">
+                <xs:sequence>
+                  <xs:element ref="gml:AbstractFeature"/>
+                </xs:sequence>
+              </xs:extension>
+            </xs:complexContent>
+          </xs:complexType>
+        </xs:element>
+      </xs:sequence>
+    </xs:extension>
+  </xs:complexContent>
+</xs:complexType>
+<xs:element name="concave_hull_points_07_qgis" type="ogr:concave_hull_points_07_qgis_Type" substitutionGroup="gml:AbstractFeature"/>
+<xs:complexType name="concave_hull_points_07_qgis_Type">
+  <xs:complexContent>
+    <xs:extension base="gml:AbstractFeatureType">
+      <xs:sequence>
+        <xs:element name="geometryProperty" type="gml:SurfacePropertyType" nillable="true" minOccurs="0" maxOccurs="1"/> <!-- restricted to Polygon --><!-- srsName="urn:ogc:def:crs:EPSG::4326" -->
+      </xs:sequence>
+    </xs:extension>
+  </xs:complexContent>
+</xs:complexType>
+</xs:schema>
diff --git a/python/plugins/processing/tests/testdata/qgis_algorithm_tests4.yaml b/python/plugins/processing/tests/testdata/qgis_algorithm_tests4.yaml
index 80551f05aa5..e7e3c0b48e7 100644
--- a/python/plugins/processing/tests/testdata/qgis_algorithm_tests4.yaml
+++ b/python/plugins/processing/tests/testdata/qgis_algorithm_tests4.yaml
@@ -268,37 +268,73 @@ tests:
               cast: str
             fid: skip
 
-  # concave hull tests should be upddated when CI will be using GEOS>=3.11
-  # current tests data were generated by Python implementation which produces
-  # incorrect result by not including all input points in the concave hull
-  # see https://github.com/qgis/QGIS/issues/54561
-  #- algorithm: native:concavehull
-  #  name: Concave Hull - Points (0.3)
-  #  params:
-  #    ALPHA: 0.3
-  #    HOLES: true
-  #    INPUT:
-  #      name: points.gml
-  #      type: vector
-  #    NO_MULTIGEOMETRY: false
-  #  results:
-  #    OUTPUT:
-  #      name: expected/concave_hull_points_03.gml
-  #      type: vector
+  - algorithm: native:concavehull
+    name: Concave Hull - Points (0.3) (GEOS <= 3.10)
+    condition:
+      geos:
+        less_than: 31100
+    params:
+      ALPHA: 0.3
+      HOLES: true
+      INPUT:
+        name: points.gml
+        type: vector
+      NO_MULTIGEOMETRY: false
+    results:
+      OUTPUT:
+        name: expected/concave_hull_points_03_qgis.gml
+        type: vector
 
-  #- algorithm: native:concavehull
-  #  name: Concave Hull - Points (0.7)
-  #  params:
-  #    ALPHA: 0.7
-  #    HOLES: true
-  #    INPUT:
-  #      name: points.gml
-  #      type: vector
-  #    NO_MULTIGEOMETRY: false
-  #  results:
-  #    OUTPUT:
-  #      name: expected/concave_hull_points_07.gml
-  #      type: vector
+  - algorithm: native:concavehull
+    name: Concave Hull - Points (0.7) (GEOS <= 3.10)
+    condition:
+      geos:
+        less_than: 31100
+    params:
+      ALPHA: 0.7
+      HOLES: true
+      INPUT:
+        name: points.gml
+        type: vector
+      NO_MULTIGEOMETRY: false
+    results:
+      OUTPUT:
+        name: expected/concave_hull_points_07_qgis.gml
+        type: vector
+
+  - algorithm: native:concavehull
+    name: Concave Hull - Points (0.3) (GEOS > 3.11)
+    condition:
+      geos:
+        at_least: 31100
+    params:
+      ALPHA: 0.3
+      HOLES: true
+      INPUT:
+        name: points.gml
+        type: vector
+      NO_MULTIGEOMETRY: false
+    results:
+      OUTPUT:
+        name: expected/concave_hull_points_03_geos.gml
+        type: vector
+
+  - algorithm: native:concavehull
+    name: Concave Hull - Points (0.7) (GEOS > 3.11)
+    condition:
+      geos:
+        at_least: 31100
+    params:
+      ALPHA: 0.7
+      HOLES: true
+      INPUT:
+        name: points.gml
+        type: vector
+      NO_MULTIGEOMETRY: false
+    results:
+      OUTPUT:
+        name: expected/concave_hull_points_07_geos.gml
+        type: vector
 
   - algorithm: qgis:knearestconcavehull
     name: K-nearest Neighbor Concave Hull - Points (k=7)