diff --git a/cmake/CMakeLists.txt b/cmake/CMakeLists.txt
index b075fc8f8d..95d738d279 100644
--- a/cmake/CMakeLists.txt
+++ b/cmake/CMakeLists.txt
@@ -159,17 +159,20 @@ endif()
 ########################################################################
 # User input options                                                   #
 ########################################################################
-# set path to python interpreter and thus enforcing python version when
-# in a virtual environment and PYTHON_EXECUTABLE is not set on command line
-if(DEFINED ENV{VIRTUAL_ENV} AND NOT PYTHON_EXECUTABLE)
-  if(CMAKE_HOST_SYSTEM_NAME STREQUAL "Windows")
-    set(PYTHON_EXECUTABLE "$ENV{VIRTUAL_ENV}/Scripts/python.exe")
-  else()
-    set(PYTHON_EXECUTABLE "$ENV{VIRTUAL_ENV}/bin/python")
-  endif()
+# backward compatibility with CMake before 3.12 and older LAMMPS documentation
+if (PYTHON_EXECUTABLE)
   set(Python_EXECUTABLE "${PYTHON_EXECUTABLE}")
+endif()
+# set path to python interpreter and thus enforcing python version when
+# in a virtual environment and Python_EXECUTABLE is not set on command line
+if(DEFINED ENV{VIRTUAL_ENV} AND NOT Python_EXECUTABLE)
+  if(CMAKE_HOST_SYSTEM_NAME STREQUAL "Windows")
+    set(Python_EXECUTABLE "$ENV{VIRTUAL_ENV}/Scripts/python.exe")
+  else()
+    set(Python_EXECUTABLE "$ENV{VIRTUAL_ENV}/bin/python")
+  endif()
   message(STATUS "Running in virtual environment: $ENV{VIRTUAL_ENV}\n"
-    "   Setting Python interpreter to: ${PYTHON_EXECUTABLE}")
+    "   Setting Python interpreter to: ${Python_EXECUTABLE}")
 endif()
 
 set(LAMMPS_MACHINE "" CACHE STRING "Suffix to append to lmp binary (WON'T enable any features automatically")
@@ -794,9 +797,6 @@ install(
 ###############################################################################
 if(BUILD_SHARED_LIBS)
   # backward compatibility
-  if(PYTHON_EXECUTABLE)
-    set(Python_EXECUTABLE ${PYTHON_EXECUTABLE})
-  endif()
   find_package(Python COMPONENTS Interpreter)
   if(BUILD_IS_MULTI_CONFIG)
     set(MY_BUILD_DIR ${CMAKE_BINARY_DIR}/$<CONFIG>)
diff --git a/cmake/Modules/Packages/PYTHON.cmake b/cmake/Modules/Packages/PYTHON.cmake
index 59260e39d5..e05edadbf3 100644
--- a/cmake/Modules/Packages/PYTHON.cmake
+++ b/cmake/Modules/Packages/PYTHON.cmake
@@ -1,6 +1,6 @@
 
 if(NOT Python_INTERPRETER)
-  # backward compatibility
+  # backward compatibility with CMake before 3.12 and older LAMMPS documentation
   if(PYTHON_EXECUTABLE)
     set(Python_EXECUTABLE ${PYTHON_EXECUTABLE})
   endif()
diff --git a/doc/src/Build_extras.rst b/doc/src/Build_extras.rst
index 393d7e1c20..7a7b5cf0d5 100644
--- a/doc/src/Build_extras.rst
+++ b/doc/src/Build_extras.rst
@@ -1056,12 +1056,12 @@ additional details.
 
       .. code-block:: bash
 
-         -D PYTHON_EXECUTABLE=path   # path to Python executable to use
+         -D Python_EXECUTABLE=path   # path to Python executable to use
 
       Without this setting, CMake will guess the default Python version
       on your system.  To use a different Python version, you can either
       create a virtualenv, activate it and then run cmake.  Or you can
-      set the PYTHON_EXECUTABLE variable to specify which Python
+      set the Python_EXECUTABLE variable to specify which Python
       interpreter should be used.  Note note that you will also need to
       have the development headers installed for this version,
       e.g. python2-devel.
diff --git a/doc/src/Howto_pylammps.rst b/doc/src/Howto_pylammps.rst
index 2db61cd5bb..bce37d5ac7 100644
--- a/doc/src/Howto_pylammps.rst
+++ b/doc/src/Howto_pylammps.rst
@@ -133,7 +133,7 @@ to the location in the virtual environment with:
 
 .. code-block:: bash
 
-   cmake . -DPYTHON_EXECUTABLE=$(which python)
+   cmake . -DPython_EXECUTABLE=$(which python)
 
    # install LAMMPS package in virtualenv
    (testing) make install-python