diff --git a/Modules/Core/Transform/include/itkSimilarity3DTransform.hxx b/Modules/Core/Transform/include/itkSimilarity3DTransform.hxx
index a598363e8dd..51b9c245625 100644
--- a/Modules/Core/Transform/include/itkSimilarity3DTransform.hxx
+++ b/Modules/Core/Transform/include/itkSimilarity3DTransform.hxx
@@ -62,6 +62,7 @@ Similarity3DTransform<TParametersValueType>::SetScale(ScaleType scale)
 {
   m_Scale = scale;
   this->ComputeMatrix();
+  this->ComputeOffset();
 }
 
 // Directly set the matrix
diff --git a/Modules/Core/Transform/test/CMakeLists.txt b/Modules/Core/Transform/test/CMakeLists.txt
index 37f53b7af07..b135cce2091 100644
--- a/Modules/Core/Transform/test/CMakeLists.txt
+++ b/Modules/Core/Transform/test/CMakeLists.txt
@@ -189,6 +189,7 @@ set(ITKTransformGTests
   itkBSplineTransformGTest.cxx
   itkEuler3DTransformGTest.cxx
   itkMatrixOffsetTransformBaseGTest.cxx
+  itkSimilarityTransformGTest.cxx
   itkTranslationTransformGTest.cxx
 )
 CreateGoogleTestDriver(ITKTransform "${ITKTransform-Test_LIBRARIES}" "${ITKTransformGTests}")
diff --git a/Modules/Core/Transform/test/itkSimilarityTransformGTest.cxx b/Modules/Core/Transform/test/itkSimilarityTransformGTest.cxx
new file mode 100644
index 00000000000..c3bc55b1742
--- /dev/null
+++ b/Modules/Core/Transform/test/itkSimilarityTransformGTest.cxx
@@ -0,0 +1,66 @@
+/*=========================================================================
+ *
+ *  Copyright NumFOCUS
+ *
+ *  Licensed under the Apache License, Version 2.0 (the "License");
+ *  you may not use this file except in compliance with the License.
+ *  You may obtain a copy of the License at
+ *
+ *         http://www.apache.org/licenses/LICENSE-2.0.txt
+ *
+ *  Unless required by applicable law or agreed to in writing, software
+ *  distributed under the License is distributed on an "AS IS" BASIS,
+ *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ *  See the License for the specific language governing permissions and
+ *  limitations under the License.
+ *
+ *=========================================================================*/
+
+// First include the header file to be tested:
+#include "itkSimilarity2DTransform.h"
+#include "itkSimilarity3DTransform.h"
+
+#include <gtest/gtest.h>
+
+
+namespace
+{
+
+template <typename TTransform>
+void
+Test_SetCenterAndScale()
+{
+  using PointType = typename TTransform::InputPointType;
+
+  const auto transform = TTransform::New();
+
+  for (double center{ -1.0 }; center <= 1.0; ++center)
+  {
+    transform->SetCenter(PointType(center));
+
+    for (double scale{ 0.5 }; scale <= 2.0; scale *= 2.0)
+    {
+      transform->SetScale(scale);
+
+      for (double input{ -1.0 }; input <= 1.0; ++input)
+      {
+        EXPECT_EQ(transform->TransformPoint(PointType(input)), PointType(center + (scale * (input - center))));
+      }
+    }
+  }
+}
+
+} // namespace
+
+
+// Tests that `transform->TransformPoint` yields the expected result, when
+// setting both the center and the scale (in that specific order), of the
+// similarity transform. Note that in previous versions of ITK (including
+// ITK 5.2.0), Similarity3DTransform did sometimes produce an incorrect result,
+// as reported at https://github.com/InsightSoftwareConsortium/ITK/issues/2629
+// "Similarity3DTransform::SetScale should recompute m_Offset"
+TEST(SimilarityTransform, SetCenterAndScale)
+{
+  Test_SetCenterAndScale<itk::Similarity2DTransform<>>();
+  Test_SetCenterAndScale<itk::Similarity3DTransform<>>();
+}