Thompson spent the offseason rehabbing his knee. He was expected to be healthy in time for Florida's season opener on February 15.
Pigott and Tucker graduated following the 2012 season.
Thompson's departure means the Gators will break in three new starting outfielders this season. Shafer will likely be in the outfield, but his position hasn't been determined. The Florida coaches trust him in any of the three spots.
Freshmen Christian Dicks, Cody Fulton and Harrison Bader, who is an impressive athlete that can play center field defensively, could also factor into the outfield.
FightinGators' Allison Banko first reported the story on Twitter Wednesday afternoon.