Finney-Smith made the announcement Thursday, giving the Gators some good news a week after guard Michael Frazier II opted to turn pro.
A second-team All-Southeastern Conference selection, Finney-Smith was coach Billy Donovan's most versatile player in a losing season. He was suspended three games in February for an undisclosed violation of team rules, but was otherwise Florida's most dependable player.
The 6-foot-8 Finney-Smith averaged 13.1 points and 6.2 rebounds this season.
The Gators are still awaiting word on forward/center Chris Walker's future. Walker is considering making the jump to the NBA.
With Finney-Smith back, Florida will have an experienced player to rebuild around.