Real estate sources tell TMZ the deal was finalized Wednesday for the 7-bedroom, 6-bathroom, 7,667-square-foot home which is set behind a private gate comes with a massive yard, wine cellar, and a billiards room.

The new owners will be able to enjoy a large pool, plenty of lounge and entertaining space, an outdoor Grotto kitchen and a detached guest house with a full bedroom, bathroom, and complete view of the property.

Logan bought the house in 2017 for $6.6 million and remastered and renovated the pad while living in it. While the profit isn't as big as he first wanted -- he listed it for $8.995M -- $1M turnaround ain't bad.

We broke the story ... Logan's house hit the market last November. Paul has been very vocal in the last couple years about his desire to move to Puerto Rico for financial reasons.