He played college football for the Florida Gators and Louisiana Tech Bulldogs and was selected by the San Francisco 49ers in the sixth round of the 2016 NFL draft.

Driskel has played for the Cincinnati Bengals, Detroit Lions, Denver Broncos, Houston Texans, Arizona Cardinals, and Cleveland Browns.

[19] The 49ers previously traded tight end Vernon Davis to the Denver Broncos in exchange for the pick used to select Driskel.

[21] After a season-ending injury to Thad Lewis, Driskel competed with Christian Ponder for the third-string quarterback position.

[23] He began the season as the Bengals' third quarterback on their depth chart behind veterans Andy Dalton and A. J. McCarron.

[24] Driskel made his regular-season NFL debut on October 21, 2018, in relief of Andy Dalton in the fourth quarter in the final minutes of a 45–10 loss to the Kansas City Chiefs, completing all four of his pass attempts for 39 yards.

[31] On November 10, 2019, Driskel made his first start for the Lions against the Chicago Bears after Matthew Stafford was inactive due to injury.

[34] After suffering a hamstring injury during a loss to the Washington Redskins, Driskel was placed on injured reserve on November 30, 2019.

[36] On September 20, 2020, Driskel came in for injured starting quarterback Drew Lock in a Week 2 matchup against the Pittsburgh Steelers.

During the game, Driskel threw for 176 yards, 1 touchdown, and 1 interception before being benched in the fourth quarter of the 28–10 loss.

[46] On November 18, Driskel converted from quarterback to tight end, playing the position for the first time in his career.

[57] On January 3, 2024, the Browns announced Driskel would be the starting quarterback in their 2023-24 regular season finale, a week 18 matchup against the Cincinnati Bengals.

The Browns clinched a playoff berth the week prior, so they decided to rest some of their key starters, including quarterback Joe Flacco, for the regular season finale to avoid potential injury.