Steam - Settings - Downloads - Steam Library Folders.  
Click - Add Library Folder (Add your external drive).  
Save and Close.

Go to your Library.  
Right click on the game - Properties - Local Files.  
Click Move Install Folder...  
Choose your external drive, and click Move.  
Can play off the external, you can even move the external drive to another PC and link the library to that PC's steam and now you have it installed on whatever steam is currently booted with the external.