diff --git a/python/core/qgsfileutils.sip b/python/core/qgsfileutils.sip
index 54ae1eb8291..1c04fec9aa1 100644
--- a/python/core/qgsfileutils.sip
+++ b/python/core/qgsfileutils.sip
@@ -65,6 +65,14 @@ will be returned unchanged.
 .. seealso:: :py:func:`extensionsFromFilter()`
 
 .. seealso:: :py:func:`ensureFileNameHasExtension()`
+%End
+
+    static QString stringToSafeFilename( const QString &string );
+%Docstring
+Converts a ``string`` to a safe filename, replacing characters which are not safe
+for filenames with an '_' character.
+
+This method should be called with file names only, not complete paths.
 %End
 };
 
diff --git a/src/core/qgsfileutils.cpp b/src/core/qgsfileutils.cpp
index d1dd350d40f..2dc2efeef9e 100644
--- a/src/core/qgsfileutils.cpp
+++ b/src/core/qgsfileutils.cpp
@@ -69,3 +69,11 @@ QString QgsFileUtils::addExtensionFromFilter( const QString &fileName, const QSt
   const QStringList extensions = extensionsFromFilter( filter );
   return ensureFileNameHasExtension( fileName, extensions );
 }
+
+QString QgsFileUtils::stringToSafeFilename( const QString &string )
+{
+  QRegularExpression rx( "[^\\w\\-. ]" );
+  QString s = string;
+  s.replace( rx, QStringLiteral( "_" ) );
+  return s;
+}
diff --git a/src/core/qgsfileutils.h b/src/core/qgsfileutils.h
index 1a3455cad4a..a028e79811b 100644
--- a/src/core/qgsfileutils.h
+++ b/src/core/qgsfileutils.h
@@ -70,6 +70,14 @@ class CORE_EXPORT QgsFileUtils
      * \see ensureFileNameHasExtension()
      */
     static QString addExtensionFromFilter( const QString &fileName, const QString &filter );
+
+    /**
+     * Converts a \a string to a safe filename, replacing characters which are not safe
+     * for filenames with an '_' character.
+     *
+     * This method should be called with file names only, not complete paths.
+     */
+    static QString stringToSafeFilename( const QString &string );
 };
 
 #endif // QGSFILEUTILS_H
diff --git a/tests/src/python/test_qgsfileutils.py b/tests/src/python/test_qgsfileutils.py
index b2d7fdb8499..501b33e5569 100644
--- a/tests/src/python/test_qgsfileutils.py
+++ b/tests/src/python/test_qgsfileutils.py
@@ -55,6 +55,9 @@ class TestQgsFileUtils(unittest.TestCase):
         self.assertEqual(QgsFileUtils.addExtensionFromFilter('test.tif', 'All Files (*.*)'), 'test.tif')
         self.assertEqual(QgsFileUtils.addExtensionFromFilter('test', 'All Files (*.*)'), 'test')
 
+    def testStringToSafeFilename(self):
+        self.assertEqual(QgsFileUtils.stringToSafeFilename('my FiLe v2.0_new.tif'), 'my FiLe v2.0_new.tif')
+        self.assertEqual(QgsFileUtils.stringToSafeFilename('rendered map_final? rev (12-03-1017)_real@#$&*#%&*$!!@$%^&(*(.tif'), 'rendered map_final_ rev _12-03-1017__real____________________.tif')
 
 if __name__ == '__main__':
     unittest.main()