diff --git a/tools/cmake/app.cmake b/tools/cmake/app.cmake
index 60f9f855ff..9f62df8204 100644
--- a/tools/cmake/app.cmake
+++ b/tools/cmake/app.cmake
@@ -16,7 +16,9 @@ include(mbed_set_post_build)
 # Load toolchain file
 if(NOT CMAKE_TOOLCHAIN_FILE OR MBED_TOOLCHAIN_FILE_USED)
     set(MBED_TOOLCHAIN_FILE_USED TRUE CACHE INTERNAL "")
-    include(mbed_toolchain)
+    # We want to bring CMP0123 we set in mbed_toolchain.cmake
+    # to the whole Mbed OS.
+    include(mbed_toolchain NO_POLICY_SCOPE)
 endif()
 
 # Specify available build profiles and add options for the selected build profile
diff --git a/tools/cmake/cores/Cortex-M33-NS.cmake b/tools/cmake/cores/Cortex-M33-NS.cmake
index 8ba132bdd2..e5c3548918 100644
--- a/tools/cmake/cores/Cortex-M33-NS.cmake
+++ b/tools/cmake/cores/Cortex-M33-NS.cmake
@@ -12,13 +12,15 @@ elseif(${MBED_TOOLCHAIN} STREQUAL "ARM")
         "-mcpu=cortex-m33+nodsp"
         "-mfpu=none"
     )
-    list(APPEND link_options
-        # Necessary as the linker does not always detect
-        # the architecture from the objectfiles correctly.
-        # Also, the complete flag should be "--cpu=Cortex-M33.no_dsp.no_fp"
-        # but this currently conflicts with CMake's compiler test until fixed
-        "--cpu=Cortex-M33.no_fp"
-    )
+    if(deprecated_system_processor)
+        # Normally `--cpu` is not needed, because `armlink` can infer
+        # features from object files. But CMake versions below 3.21
+        # automatically add `--cpu=${CMAKE_SYSTEM_PROCESSOR}` which is
+        # incorrect, so as a workaround we need to add `no_fp`.
+        list(APPEND link_options
+            "--cpu=Cortex-M33.no_fp"
+        )
+    endif()
 endif()
 
 function(mbed_set_cpu_core_definitions target)
diff --git a/tools/cmake/cores/Cortex-M33.cmake b/tools/cmake/cores/Cortex-M33.cmake
index ce9db87db0..ce22f0c5eb 100644
--- a/tools/cmake/cores/Cortex-M33.cmake
+++ b/tools/cmake/cores/Cortex-M33.cmake
@@ -12,13 +12,15 @@ elseif(${MBED_TOOLCHAIN} STREQUAL "ARM")
         "-mcpu=cortex-m33+nodsp"
         "-mfpu=none"
     )
-    list(APPEND link_options
-        # Necessary as the linker does not always detect
-        # the architecture from the objectfiles correctly.
-        # Also, the complete flag should be "--cpu=Cortex-M33.no_dsp.no_fp"
-        # but this currently conflicts with CMake's compiler test until fixed
-        "--cpu=Cortex-M33.no_fp"
-    )
+    if(deprecated_system_processor)
+        # Normally `--cpu` is not needed, because `armlink` can infer
+        # features from object files. But CMake versions below 3.21
+        # automatically add `--cpu=${CMAKE_SYSTEM_PROCESSOR}` which is
+        # incorrect, so as a workaround we need to add `no_fp`.
+        list(APPEND link_options
+            "--cpu=Cortex-M33.no_fp"
+        )
+    endif()
 endif()
 
 function(mbed_set_cpu_core_definitions target)
diff --git a/tools/cmake/cores/Cortex-M4.cmake b/tools/cmake/cores/Cortex-M4.cmake
index 533da387e9..2245b01cb3 100644
--- a/tools/cmake/cores/Cortex-M4.cmake
+++ b/tools/cmake/cores/Cortex-M4.cmake
@@ -12,11 +12,15 @@ elseif(${MBED_TOOLCHAIN} STREQUAL "ARM")
         "-mcpu=cortex-m4"
         "-mfpu=none"
     )
-#Necessary as the linker does not always detect
-#the architecture from the objectfiles correctly.
-    list(APPEND link_options
-        "--cpu=Cortex-M4.no_fp"
-    )
+    if(deprecated_system_processor)
+        # Normally `--cpu` is not needed, because `armlink` can infer
+        # features from object files. But CMake versions below 3.21
+        # automatically add `--cpu=${CMAKE_SYSTEM_PROCESSOR}` which is
+        # incorrect, so as a workaround we need to add `no_fp`.
+        list(APPEND link_options
+            "--cpu=Cortex-M4.no_fp"
+        )
+    endif()
 endif()
 
 function(mbed_set_cpu_core_definitions target)
diff --git a/tools/cmake/mbed_toolchain.cmake b/tools/cmake/mbed_toolchain.cmake
index 818aee4bdd..139828921b 100644
--- a/tools/cmake/mbed_toolchain.cmake
+++ b/tools/cmake/mbed_toolchain.cmake
@@ -22,47 +22,75 @@ function(mbed_generate_options_for_linker target output_response_file_path)
     file(GENERATE OUTPUT "${CMAKE_CURRENT_BINARY_DIR}/compile_time_defs.txt" CONTENT "${_compile_definitions}\n")
     set(${output_response_file_path} @${CMAKE_CURRENT_BINARY_DIR}/compile_time_defs.txt PARENT_SCOPE)
 endfunction()
-# Set the system processor depending on the CPU core type
-if (MBED_CPU_CORE STREQUAL Cortex-A9)
-    set(CMAKE_SYSTEM_PROCESSOR cortex-a9)
-elseif (MBED_CPU_CORE STREQUAL Cortex-A5)
-    set(CMAKE_SYSTEM_PROCESSOR cortex-a5)
-elseif (MBED_CPU_CORE STREQUAL Cortex-M0+)
-    set(CMAKE_SYSTEM_PROCESSOR cortex-m0plus)
-elseif (MBED_CPU_CORE STREQUAL Cortex-M0)
-    set(CMAKE_SYSTEM_PROCESSOR cortex-m0)
-elseif (MBED_CPU_CORE STREQUAL Cortex-M1)
-    set(CMAKE_SYSTEM_PROCESSOR cortex-m1)
-elseif (MBED_CPU_CORE STREQUAL Cortex-M23-NS)
-    set(CMAKE_SYSTEM_PROCESSOR cortex-m23)
-elseif (MBED_CPU_CORE STREQUAL Cortex-M23)
-    set(CMAKE_SYSTEM_PROCESSOR cortex-m23)
-elseif (MBED_CPU_CORE STREQUAL Cortex-M3)
-    set(CMAKE_SYSTEM_PROCESSOR cortex-m3)
-elseif (MBED_CPU_CORE STREQUAL Cortex-M33-NS)
-    set(CMAKE_SYSTEM_PROCESSOR cortex-m33)
-elseif (MBED_CPU_CORE STREQUAL Cortex-M33)
-    set(CMAKE_SYSTEM_PROCESSOR cortex-m33)
-elseif (MBED_CPU_CORE STREQUAL Cortex-M33F-NS)
-    set(CMAKE_SYSTEM_PROCESSOR cortex-m33)
-elseif (MBED_CPU_CORE STREQUAL Cortex-M33F)
-    set(CMAKE_SYSTEM_PROCESSOR cortex-m33)
-elseif (MBED_CPU_CORE STREQUAL Cortex-M33FE-NS)
-    set(CMAKE_SYSTEM_PROCESSOR cortex-m33)
-elseif (MBED_CPU_CORE STREQUAL Cortex-M33FE)
-    set(CMAKE_SYSTEM_PROCESSOR cortex-m33)
-elseif (MBED_CPU_CORE STREQUAL Cortex-M4)
-    set(CMAKE_SYSTEM_PROCESSOR cortex-m4)
-elseif (MBED_CPU_CORE STREQUAL Cortex-M4F)
-    set(CMAKE_SYSTEM_PROCESSOR cortex-m4)
-elseif (MBED_CPU_CORE STREQUAL Cortex-M55)
-    set(CMAKE_SYSTEM_PROCESSOR cortex-m55)
-elseif (MBED_CPU_CORE STREQUAL Cortex-M7)
-    set(CMAKE_SYSTEM_PROCESSOR cortex-m7)
-elseif (MBED_CPU_CORE STREQUAL Cortex-M7F)
-    set(CMAKE_SYSTEM_PROCESSOR cortex-m7)
-elseif (MBED_CPU_CORE STREQUAL Cortex-M7FD)
-    set(CMAKE_SYSTEM_PROCESSOR cortex-m7)
+
+# Backward compatibility with older CMake which uses CMAKE_SYSTEM_PROCESSOR to
+# automatically add compile and link options for the Arm Compiler.
+# Note: From version 3.21, CMake by default (policy CMP0123 set to NEW) does not
+# use this macro anymore, and projects have full control over compile and link
+# options. This is because the old algorithm based on CMAKE_SYSTEM_PROCESSOR
+# is too restrictive and does not support things like Cortex-M33.no_dsp.no_fp.
+if(MBED_TOOLCHAIN STREQUAL "ARM")
+    if(NOT POLICY CMP0123)
+        # Old versions of CMake do not have CMP0123.
+        # In the future, support for old versions of CMake will be
+        # dropped from Mbed OS.
+        set(deprecated_system_processor ON)
+    else()
+        cmake_policy(GET CMP0123 policy_CMP0123)
+        if("${policy_CMP0123}" STREQUAL "")
+            # CMP0123 is unset if an old `cmake_minimum_required()` is used with a
+            # new CMake. Enable new CMP0123 to take advantage of the improvement
+            # and dismiss deprecation warnings from CMake.
+            cmake_policy(SET CMP0123 NEW)
+        elseif("${policy_CMP0123}" STREQUAL "OLD")
+            # Respect old CMP0123 forced by user application
+            set(deprecated_system_processor ON)
+        endif()
+    endif()
+endif()
+
+if(deprecated_system_processor)
+    if (MBED_CPU_CORE STREQUAL Cortex-A9)
+        set(CMAKE_SYSTEM_PROCESSOR cortex-a9)
+    elseif (MBED_CPU_CORE STREQUAL Cortex-A5)
+        set(CMAKE_SYSTEM_PROCESSOR cortex-a5)
+    elseif (MBED_CPU_CORE STREQUAL Cortex-M0+)
+        set(CMAKE_SYSTEM_PROCESSOR cortex-m0plus)
+    elseif (MBED_CPU_CORE STREQUAL Cortex-M0)
+        set(CMAKE_SYSTEM_PROCESSOR cortex-m0)
+    elseif (MBED_CPU_CORE STREQUAL Cortex-M1)
+        set(CMAKE_SYSTEM_PROCESSOR cortex-m1)
+    elseif (MBED_CPU_CORE STREQUAL Cortex-M23-NS)
+        set(CMAKE_SYSTEM_PROCESSOR cortex-m23)
+    elseif (MBED_CPU_CORE STREQUAL Cortex-M23)
+        set(CMAKE_SYSTEM_PROCESSOR cortex-m23)
+    elseif (MBED_CPU_CORE STREQUAL Cortex-M3)
+        set(CMAKE_SYSTEM_PROCESSOR cortex-m3)
+    elseif (MBED_CPU_CORE STREQUAL Cortex-M33-NS)
+        set(CMAKE_SYSTEM_PROCESSOR cortex-m33)
+    elseif (MBED_CPU_CORE STREQUAL Cortex-M33)
+        set(CMAKE_SYSTEM_PROCESSOR cortex-m33)
+    elseif (MBED_CPU_CORE STREQUAL Cortex-M33F-NS)
+        set(CMAKE_SYSTEM_PROCESSOR cortex-m33)
+    elseif (MBED_CPU_CORE STREQUAL Cortex-M33F)
+        set(CMAKE_SYSTEM_PROCESSOR cortex-m33)
+    elseif (MBED_CPU_CORE STREQUAL Cortex-M33FE-NS)
+        set(CMAKE_SYSTEM_PROCESSOR cortex-m33)
+    elseif (MBED_CPU_CORE STREQUAL Cortex-M33FE)
+        set(CMAKE_SYSTEM_PROCESSOR cortex-m33)
+    elseif (MBED_CPU_CORE STREQUAL Cortex-M4)
+        set(CMAKE_SYSTEM_PROCESSOR cortex-m4)
+    elseif (MBED_CPU_CORE STREQUAL Cortex-M4F)
+        set(CMAKE_SYSTEM_PROCESSOR cortex-m4)
+    elseif (MBED_CPU_CORE STREQUAL Cortex-M55)
+        set(CMAKE_SYSTEM_PROCESSOR cortex-m55)
+    elseif (MBED_CPU_CORE STREQUAL Cortex-M7)
+        set(CMAKE_SYSTEM_PROCESSOR cortex-m7)
+    elseif (MBED_CPU_CORE STREQUAL Cortex-M7F)
+        set(CMAKE_SYSTEM_PROCESSOR cortex-m7)
+    elseif (MBED_CPU_CORE STREQUAL Cortex-M7FD)
+        set(CMAKE_SYSTEM_PROCESSOR cortex-m7)
+    endif()
 endif()
 
 # Compiler setup