diff --git a/CMakeLists.txt b/CMakeLists.txt
index 59a960a8b6..f72de64205 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -355,7 +355,7 @@ if(NOT DISABLE_PACKAGE_CONFIG_AND_INSTALL)
     install(
         FILES "${CMAKE_CURRENT_BINARY_DIR}/cmake/MbedTLSConfig.cmake"
               "${CMAKE_CURRENT_BINARY_DIR}/cmake/MbedTLSConfigVersion.cmake"
-        DESTINATION "cmake")
+        DESTINATION "${CMAKE_INSTALL_LIBDIR}/cmake/MbedTLS")
 
     export(
         EXPORT MbedTLSTargets
@@ -365,7 +365,7 @@ if(NOT DISABLE_PACKAGE_CONFIG_AND_INSTALL)
     install(
         EXPORT MbedTLSTargets
         NAMESPACE MbedTLS::
-        DESTINATION "cmake"
+        DESTINATION "${CMAKE_INSTALL_LIBDIR}/cmake/MbedTLS"
         FILE "MbedTLSTargets.cmake")
 
     if(CMAKE_VERSION VERSION_GREATER 3.15 OR CMAKE_VERSION VERSION_EQUAL 3.15)
diff --git a/ChangeLog.d/cmake-install.txt b/ChangeLog.d/cmake-install.txt
new file mode 100644
index 0000000000..d8eb72e1ec
--- /dev/null
+++ b/ChangeLog.d/cmake-install.txt
@@ -0,0 +1,3 @@
+Changes
+  * Install the .cmake files into CMAKE_INSTALL_LIBDIR/cmake/MbedTLS,
+    typically /usr/lib/cmake/MbedTLS.
diff --git a/programs/test/cmake_package_install/CMakeLists.txt b/programs/test/cmake_package_install/CMakeLists.txt
index 711a1e506e..fb5ad51b54 100644
--- a/programs/test/cmake_package_install/CMakeLists.txt
+++ b/programs/test/cmake_package_install/CMakeLists.txt
@@ -26,7 +26,7 @@ execute_process(
 # Locate the package.
 #
 
-set(MbedTLS_DIR "${MbedTLS_INSTALL_DIR}/cmake")
+list(INSERT CMAKE_PREFIX_PATH 0 "${MbedTLS_INSTALL_DIR}")
 find_package(MbedTLS REQUIRED)
 
 #