Gannon attended the University of Delaware where he was a member of Sigma Phi Epsilon. In football, he was coached by Tubby Raymond and played within Raymond’s wing T offense. With the Delaware Fightin’ Blue Hens football team, Gannon first played as a punter before switching to quarterback in sophomore year. Gannon set 21 school records, including total offense (7,432 yards), passing yards (5,927), pass attempts (845), and completions (462) and was the only Delaware player at the time to achieve at least 2,000 yards of offense three years in a row. As a sophomore, Gannon won the Eastern College Athletic Conference Division I-AA Rookie of the Year award in 1984. In 1986, during his senior season, Gannon won Yankee Conference Offensive Player of the Year honors and was an honorable mention All-American selection.

For the 1988 season, Gannon was third-string after Wade Wilson and Tommy Kramer. Gannon played three games in 1988. In a Week 5 (October 2) 24–7 loss to the Miami Dolphins, Gannon completed 7 of 15 passes for 90 yards but was sacked twice for 15. He also rushed twice for 15 yards. Gannon took a knee in the Vikings’ Week 8 (October 23) victory over the Tampa Bay Buccaneers. In Week 10 (November 6), Gannon was sacked for 7 yards and rushed for 15 yards in a 44–17 win over the Detroit Lions. Improving from 1987, the 1988 Vikings finished 11–5 and advanced to the divisional round of the playoffs.

Gannon started his first game in Week 4 (September 30) of 1990 after Wade Wilson had torn thumb ligaments. The Vikings lost that game to the Tampa Bay Buccaneers in overtime 23–20. Steve Christie kicked the winning field goal for Tampa in a drive started from a Wayne Haddix interception of a Gannon pass. Gannon would play 14 games in 1990 and start 12.

In Week 7 (October 15), Gannon started against the Detroit Lions and completed 8 of 10 passes for 146 yards and two touchdowns for a 24–0 lead. Salisbury took over in the second quarter after Gannon suffered a hyperextended left knee, and the Vikings beat the Lions 31–14. The Vikings now were a surprising 5–1 after going a combined 14–18 in the 1990 and 1991 seasons.

In the 1991 preseason, Vikings coach Jerry Burns demoted Gannon to third-string and elevated Sean Salisbury to second-string behind Wade Wilson. Gannon played his first game of the year in Week 5 (September 29) against the Denver Broncos, replacing Wade Wilson with 7:20 left in the fourth quarter after Wilson threw three interceptions. On fourth down at Denver’s 13-yard line with 43 seconds left, a wide-open Hassan Jones dropped Gannon’s pass, and Minnesota lost 13–6. Gannon would replace Wilson as starter for the last 11 games of 1991, and the Vikings went 6–5 with Gannon as starter for an overall 8–8 season. Gannon was 211-for-354 in completed passes for 2,166 yards, 12 touchdowns, and 6 interceptions. He was sacked 19 times for 91 yards and rushed 43 times for 236 yards, including two rushing touchdowns.

On August 19, 1993, the Vikings traded Gannon to the Washington Redskins for a conditional 1994 fifth-round draft pick. Gannon was the third-stringer behind starter Mark Rypien and backup Cary Conklin. With the Redskins, Gannon played in eight games and started the four games from Weeks 12 to 15.

Gannon sat out the 1994 season after shoulder surgery. In 1995, Gannon signed with the Kansas City Chiefs. For two years he served as a backup to Steve Bono. In 1997 a quarterback controversy was created when the Gannon-led Chiefs excelled in the absence of the injured Elvis Grbac. In the playoffs, coach Marty Schottenheimer elected to play Grbac instead of Gannon, and the Chiefs lost 14–10. The two ended up splitting snaps in 1998, after Grbac was injured in Week 1.

In February 1999 Gannon was signed as a free agent by the Oakland Raiders. He excelled in head coach Jon Gruden’s West Coast offense and was voted to the Pro Bowl in his first year as a Raider – the first of four straight selections. In 2001 and 2002 he won the Pro Bowl MVP award consecutively, a feat achieved by no other NFL player.

When he led the Raiders to Super Bowl XXXVII in 2003, he was the second player from the University of Delaware to go to the Super Bowl.

Gannon’s 2003 season was ended by a shoulder injury in Week 7 after a 2–5 start. A serious neck injury in 2004 effectively ended his career. Gannon was hurt in Week 3 when he scrambled, and slid into a helmet-to-helmet collision with Tampa Bay linebacker Derrick Brooks.

On August 6, 2005, Gannon officially retired from football and joined CBS television as an NFL analyst. He was inducted into the University of Delaware athletics hall of fame the same year.

Gannon joined CBS Sports as an NFL game analyst in August 2005. He also works as a game analyst for Green Bay Packers preseason games.