diff --git a/CMakeLists.txt b/CMakeLists.txt
index 623d9a6516a..71d69e21621 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -705,9 +705,14 @@ add_definitions(-DQT_DISABLE_DEPRECATED_BEFORE=0x050800)
 # For fast string concatenation
 add_definitions(-DQT_USE_QSTRINGBUILDER)
 
-if (WITH_GEOREFERENCER OR WITH_ANALYSIS)
+set(WITH_GSL TRUE CACHE BOOL "Determines whether GSL library should be used")
+
+if (WITH_ANALYSIS AND WITH_GSL)
   find_package(GSL REQUIRED)
-  set(HAVE_GEOREFERENCER TRUE)
+  set(HAVE_GSL TRUE)
+  if (WITH_GEOREFERENCER)
+    set(HAVE_GEOREFERENCER TRUE)
+  endif()
 endif()
 
 if(ENABLE_COVERAGE)
diff --git a/cmake_templates/qgsconfig.h.in b/cmake_templates/qgsconfig.h.in
index a8fa97d4bba..b5e01a5808d 100644
--- a/cmake_templates/qgsconfig.h.in
+++ b/cmake_templates/qgsconfig.h.in
@@ -76,6 +76,8 @@
 
 #cmakedefine HAVE_3D
 
+#cmakedefine HAVE_GSL
+
 #cmakedefine HAVE_GEOREFERENCER
 
 #cmakedefine USE_THREAD_LOCAL
diff --git a/python/CMakeLists.txt b/python/CMakeLists.txt
index 3681af82845..da1d46cc327 100644
--- a/python/CMakeLists.txt
+++ b/python/CMakeLists.txt
@@ -258,6 +258,7 @@ if(WITH_ANALYSIS)
 
   # analysis module
   file(GLOB_RECURSE sip_files_analysis analysis/*.sip analysis/*.sip.in)
+
   set(SIP_EXTRA_FILES_DEPEND ${sip_files_core} ${sip_files_analysis})
   set(SIP_EXTRA_OPTIONS ${PYQT_SIP_FLAGS} -g -o -a ${CMAKE_BINARY_DIR}/python/qgis.analysis.api)
   if((${SIP_VERSION_STR} VERSION_EQUAL 4.19.11) OR (${SIP_VERSION_STR} VERSION_GREATER 4.19.11))
diff --git a/src/analysis/CMakeLists.txt b/src/analysis/CMakeLists.txt
index 89ac88e3c63..56f698adfce 100644
--- a/src/analysis/CMakeLists.txt
+++ b/src/analysis/CMakeLists.txt
@@ -401,10 +401,13 @@ find_package(EXIV2 REQUIRED)
 include_directories(SYSTEM ${SPATIALITE_INCLUDE_DIR})
 include_directories(SYSTEM ${SPATIALINDEX_INCLUDE_DIR})
 include_directories(SYSTEM ${SQLITE3_INCLUDE_DIR})
-include_directories(SYSTEM ${GSL_INCLUDE_DIR})
 include_directories(BEFORE raster)
 include_directories(BEFORE mesh)
 
+if(HAVE_GSL)
+  include_directories(SYSTEM ${GSL_INCLUDE_DIR})
+endif()
+
 ADD_FLEX_FILES_PREFIX(QGIS_ANALYSIS_SRCS raster raster/qgsrastercalclexer.ll)
 ADD_BISON_FILES_PREFIX(QGIS_ANALYSIS_SRCS raster raster/qgsrastercalcparser.yy)
 
@@ -520,9 +523,12 @@ target_link_libraries(
   qgis_analysis
   qgis_core
   ${EXIV2_LIBRARY}
-  ${GSL_LIBRARIES}
   )
 
+if(HAVE_GSL)
+  target_link_libraries(qgis_analysis ${GSL_LIBRARIES})
+endif()
+
 if(HAVE_OPENCL)
     target_link_libraries(qgis_analysis ${OpenCL_LIBRARIES})
 endif()
diff --git a/src/analysis/georeferencing/qgsleastsquares.cpp b/src/analysis/georeferencing/qgsleastsquares.cpp
index dd74bc94411..a6d64c978d5 100644
--- a/src/analysis/georeferencing/qgsleastsquares.cpp
+++ b/src/analysis/georeferencing/qgsleastsquares.cpp
@@ -12,16 +12,20 @@
  *   (at your option) any later version.                                   *
  *                                                                         *
  ***************************************************************************/
-#include <cmath>
-#include <stdexcept>
 
-#include <gsl/gsl_linalg.h>
-#include <gsl/gsl_blas.h>
+#include "qgsleastsquares.h"
+#include "qgsconfig.h"
+#include "qgsexception.h"
 
 #include <QObject>
 
-#include "qgsleastsquares.h"
+#include <cmath>
+#include <stdexcept>
 
+#ifdef HAVE_GSL
+#include <gsl/gsl_linalg.h>
+#include <gsl/gsl_blas.h>
+#endif
 
 void QgsLeastSquares::linear( const QVector<QgsPointXY> &sourceCoordinates,
                               const QVector<QgsPointXY> &destinationCoordinates,
@@ -67,6 +71,14 @@ void QgsLeastSquares::helmert( const QVector<QgsPointXY> &sourceCoordinates,
                                QgsPointXY &origin, double &pixelSize,
                                double &rotation )
 {
+#ifndef HAVE_GSL
+  ( void )sourceCoordinates;
+  ( void )destinationCoordinates;
+  ( void )origin;
+  ( void )pixelSize;
+  ( void )rotation;
+  throw QgsNotSupportedException( QStringLiteral( "Calculating a helmert transformation requires a QGIS build based GSL" ) );
+#else
   int n = destinationCoordinates.size();
   if ( n < 2 )
   {
@@ -125,6 +137,7 @@ void QgsLeastSquares::helmert( const QVector<QgsPointXY> &sourceCoordinates,
   pixelSize = std::sqrt( std::pow( gsl_vector_get( x, 0 ), 2 ) +
                          std::pow( gsl_vector_get( x, 1 ), 2 ) );
   rotation = std::atan2( gsl_vector_get( x, 1 ), gsl_vector_get( x, 0 ) );
+#endif
 }
 
 #if 0
@@ -245,6 +258,12 @@ void QgsLeastSquares::projective( const QVector<QgsPointXY> &sourceCoordinates,
                                   const QVector<QgsPointXY> &destinationCoordinates,
                                   double H[9] )
 {
+#ifndef HAVE_GSL
+  ( void )sourceCoordinates;
+  ( void )destinationCoordinates;
+  ( void )H;
+  throw QgsNotSupportedException( QStringLiteral( "Calculating a projective transformation requires a QGIS build based GSL" ) );
+#else
   Q_ASSERT( sourceCoordinates.size() == destinationCoordinates.size() );
 
   if ( destinationCoordinates.size() < 4 )
@@ -341,4 +360,5 @@ void QgsLeastSquares::projective( const QVector<QgsPointXY> &sourceCoordinates,
   gsl_matrix_free( V );
   gsl_vector_free( singular_values );
   gsl_vector_free( work );
+#endif
 }
diff --git a/src/analysis/georeferencing/qgsleastsquares.h b/src/analysis/georeferencing/qgsleastsquares.h
index 6beb6e8b1d0..8a6a2853a10 100644
--- a/src/analysis/georeferencing/qgsleastsquares.h
+++ b/src/analysis/georeferencing/qgsleastsquares.h
@@ -42,6 +42,7 @@ class ANALYSIS_EXPORT QgsLeastSquares
 
     /**
      * Transforms the point at \a origin in-place, using a helmert transformation calculated from the list of source and destination Ground Control Points (GCPs).
+     * \throws QgsNotSupportedException on QGIS built without GSL.
      */
     static void helmert( const QVector<QgsPointXY> &sourceCoordinates,
                          const QVector<QgsPointXY> &destinationCoordinates,
@@ -55,6 +56,7 @@ class ANALYSIS_EXPORT QgsLeastSquares
 
     /**
      * Calculates projective parameters from the list of source and destination Ground Control Points (GCPs).
+     * \throws QgsNotSupportedException on QGIS built without GSL.
      */
     static void projective( const QVector<QgsPointXY> &sourceCoordinates,
                             const QVector<QgsPointXY> &destinationCoordinates,
diff --git a/tests/src/analysis/CMakeLists.txt b/tests/src/analysis/CMakeLists.txt
index f659354b353..180257e23af 100644
--- a/tests/src/analysis/CMakeLists.txt
+++ b/tests/src/analysis/CMakeLists.txt
@@ -48,7 +48,6 @@ endmacro (ADD_QGIS_TEST)
 #############################################################
 # Tests:
 set(TESTS
- testqgsgcptransformer.cpp
  testqgsgeometrysnapper.cpp
  testqgsinterpolator.cpp
  testqgsprocessing.cpp
@@ -64,6 +63,13 @@ set(TESTS
  testqgstriangulation.cpp
 )
 
+if(HAVE_GSL)
+  set(TESTS
+    ${TESTS}
+    testqgsgcptransformer.cpp
+    )
+endif()
+
 foreach(TESTSRC ${TESTS})
     ADD_QGIS_TEST(${TESTSRC})
 endforeach(TESTSRC)