Officials at Kentucky had been courting Donovan to take over that storied program but the coach issued a statement expressing his intention not to move.
Donovan's Gators on Monday won their second consecutive tournament title, beating Ohio State. Last year Florida topped UCLA in winning the championship.
Donovan was an assistant at Kentucky for five seasons under Rick Pitino and had been mentioned for the Wildcats' job since Tubby Smith resigned and left for the Minnesota Golden Gophers.
Florida finished this last season 33-5 and is 261-103 under Donovan. The Gators have been top the Final Four three times since he took over that program.