The Obamas got the keys Wednesday for the awesome mansion which sits on 29 acres of beachfront property. TMZ broke the story back in August when the former Prez and First Lady were in escrow on the luxurious home ... formerly owned by Celtics owner Wyc Grousbeck.

As we told you, it was listed for $14,850,000 ... but our sources told us the Obamas were paying much less. Now we know how much less. According to real estate records, they're plunking down $11.75 million.

That kinda dough gets them 6,900 square feet with 7 bedrooms. The enormous pad has a pool, outdoor fireplace, and vaulted ceilings. It also has 2 guest wings off the main home.

Michelle and Barack test drove the house over the summer ... when they were renting it. Obviously, they were impressed and decided to make it permanent.

Tom LeClair and Gerret Conover of Landvest were realtors for the transaction. We reached out, but they had no comment.

Congrats to the new homeowners! Did we mention their estate comes with a private beach and a boathouse?