diff --git a/CMakeLists.txt b/CMakeLists.txt
index 4d0496b19..803b830b4 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -1,11 +1,11 @@
 cmake_minimum_required (VERSION 3.0)
 
+project (fftw VERSION 3.3.10 LANGUAGES C)
+
 if (NOT DEFINED CMAKE_BUILD_TYPE)
   set (CMAKE_BUILD_TYPE Release CACHE STRING "Build type")
 endif ()
 
-project (fftw)
-
 if (POLICY CMP0042)
   cmake_policy (SET CMP0042 NEW)
 endif ()
@@ -279,8 +279,6 @@ if (HAVE_AVX2)
   list (APPEND SOURCEFILES ${fftw_dft_simd_avx2_SOURCE} ${fftw_rdft_simd_avx2_SOURCE})
 endif ()
 
-set (FFTW_VERSION 3.3.10)
-
 set (PREC_SUFFIX)
 if (ENABLE_FLOAT)
   set (FFTW_SINGLE TRUE)
@@ -370,7 +368,7 @@ if (OPENMP_FOUND)
 endif ()
 
 foreach(subtarget ${subtargets})
-  set_target_properties (${subtarget} PROPERTIES SOVERSION 3.6.9 VERSION 3)
+  set_target_properties (${subtarget} PROPERTIES VERSION ${PROJECT_VERSION} SOVERSION ${PROJECT_VERSION_MAJOR})
   install (TARGETS ${subtarget}
 	  RUNTIME DESTINATION ${CMAKE_INSTALL_BINDIR}
 	  LIBRARY DESTINATION ${CMAKE_INSTALL_LIBDIR}
@@ -424,7 +422,7 @@ set (prefix ${CMAKE_INSTALL_PREFIX})
 set (exec_prefix ${CMAKE_INSTALL_PREFIX})
 set (libdir ${CMAKE_INSTALL_FULL_LIBDIR})
 set (includedir ${CMAKE_INSTALL_FULL_INCLUDEDIR})
-set (VERSION ${FFTW_VERSION})
+set (VERSION ${PROJECT_VERSION})
 configure_file (fftw.pc.in fftw3${PREC_SUFFIX}.pc @ONLY)
 install (FILES
           ${CMAKE_CURRENT_BINARY_DIR}/fftw3${PREC_SUFFIX}.pc
diff --git a/FFTW3ConfigVersion.cmake.in b/FFTW3ConfigVersion.cmake.in
index cb906a406..1a5eaca3f 100644
--- a/FFTW3ConfigVersion.cmake.in
+++ b/FFTW3ConfigVersion.cmake.in
@@ -1,5 +1,5 @@
 
-set (PACKAGE_VERSION "@FFTW_VERSION@")
+set (PACKAGE_VERSION "@PROJECT_VERSION@")
 
 # Check whether the requested PACKAGE_FIND_VERSION is compatible
 if ("${PACKAGE_VERSION}" VERSION_LESS "${PACKAGE_FIND_VERSION}")
diff --git a/Makefile.am b/Makefile.am
index eaf131cca..227bca66f 100644
--- a/Makefile.am
+++ b/Makefile.am
@@ -151,7 +151,7 @@ FFTW3@PREC_SUFFIX@Config.cmake: $(top_srcdir)/FFTW3Config.cmake.in
 		$(top_srcdir)/FFTW3Config.cmake.in > $@
 FFTW3@PREC_SUFFIX@ConfigVersion.cmake: $(top_srcdir)/FFTW3ConfigVersion.cmake.in
 	$(SED) \
-		-e 's|[@]FFTW_VERSION@|@PACKAGE_VERSION@|g' \
+		-e 's|[@]PROJECT_VERSION@|@PACKAGE_VERSION@|g' \
 		$(top_srcdir)/FFTW3ConfigVersion.cmake.in > $@
 cmakedir = $(libdir)/cmake/fftw3
 cmake_DATA = FFTW3@PREC_SUFFIX@Config.cmake FFTW3@PREC_SUFFIX@ConfigVersion.cmake
diff --git a/cmake.config.h.in b/cmake.config.h.in
index 1f4c50559..c3e4cc99f 100644
--- a/cmake.config.h.in
+++ b/cmake.config.h.in
@@ -294,7 +294,7 @@
 #define PACKAGE_NAME "fftw"
 
 /* Define to the full name and version of this package. */
-#define PACKAGE_STRING "fftw @FFTW_VERSION@"
+#define PACKAGE_STRING "fftw @PROJECT_VERSION@"
 
 /* Define to the one symbol short name of this package. */
 #define PACKAGE_TARNAME "fftw"
@@ -303,7 +303,7 @@
 #define PACKAGE_URL ""
 
 /* Define to the version of this package. */
-#define PACKAGE_VERSION "@FFTW_VERSION@"
+#define PACKAGE_VERSION "@PROJECT_VERSION@"
 
 /* Define to necessary symbol if this constant uses a non-standard name on
    your system. */
@@ -366,7 +366,7 @@
 #cmakedefine USING_POSIX_THREADS 1
 
 /* Version number of package */
-#define VERSION "@FFTW_VERSION@"
+#define VERSION "@PROJECT_VERSION@"
 
 /* Use common Windows Fortran mangling styles for the Fortran interfaces. */
 /* #undef WINDOWS_F77_MANGLING */