1. Log into the Steam client.
2. Go to your LIBRARY and click "+ ADD A GAME" in the bottom-left corner.
3. Select "Add a Non-Steam Game."
4. Click FINAL FANTASY XIV Online in the list of displayed programs and click on "ADD SELECTED PROGRAMS."

The game will now be displayed in your Steam games library and you can use the Steam Overlay while playing by pressing the Shift+Tab keys.

Please note that this will not change the registration type of the version registered on the Mog Station. You will continue to need to purchase and register the Windows version of the game to the account and Steam registration codes will not be valid to register on the same service account.