Driskel accepted an athletic scholarship to attend the University of Florida, where he has played for coach Will Muschamp's Florida Gators football since 2011. As a freshman, Driskel appeared in five games, completing 16 of 34 passes for 148 yards with two interceptions. He became the team's starter as a sophomore in 2012. He led them to an 11-2 record and a berth in the 2013 Sugar Bowl, in which Florida lost to Teddy Bridgewater and the Louisville Cardinals.
After starting three games in 2013, Driskel broke his right fibula in a football game against the University of Tennessee and missed the remainder of the season. Prior to the start of the 2014 college football season, Driskel was put on the Maxwell Award and Davey O'Brien award watch-lists. Additionally, Driskel was named to Phil Steele's pre-season 3rd Team All-American list.