Sweat led the Seminoles in sacks this season with 5.5 and finished second on the team with 12.5 tackles for loss.
Sweat was the No. 1 prospect in the Class of 2015 entering his senior year of high school, but dislocated his knee and tore his ACL in the third game of that season.
He still ranked as the No. 3 defensive end recruit in the 2015 signing class and No. 11 overall in the 2015 ESPN 300.
He received regular playing time on the FSU defensive line in each of his three years in Tallahassee.
"This was a very tough decision for me, and one that I didn't take lightly," Sweat said Thursday in the statement. "It has truly been an honor and a pleasure to wear the Garnet and Gold for three seasons."
Sweat is the third underclassman from Florida State to announce he's leaving early for the NFL draft, joining safety Derwin James and tight end Ryan Izzo. Several others, including cornerback Tarvarus McFadden, are also contemplating a departure.