I don’t think he has that power. We own the base by treaty. The President cannot singlehandedly abrogate a treaty.
Here’s how he does it:
http://www.huffingtonpost.com/joseph-v-micallef/could-barack-obama-give-t_b_9334352.html
Says that the US had no authority to the 1934 treaty and signs an executive order withdrawing from the treaty.
Gives Gitmo back to Cuba.
And IIRC, I believe Castro said there would be no easing of relations unless the USA agreed to give it back. And we know there has been an easing.
The treaty was for 100 years and expired in the 1990s.