Kelly was a successful collegiate quarterback at the University of Tennessee from 1988–1991 under head coach Johnny Majors. He took over as a starter for Sterling Henton in the 1989 SECrivalry game against the AlabamaCrimson Tide. He became part of Tennessee football lore as part of team that accomplished a 35–34 at Notre Dame, later dubbed as "The Miracle at South Bend". The Vols trailed at one point 31–7 before Kelly helped instrument a comeback to beat the Fighting Irish. He set numerous Tennessee and SEC passing records, most of them broken by his later successor at Tennessee, Peyton Manning.
Kelly's predominant professional football career was as an Arena Football League quarterback, playing some of his career with the New Orleans VooDoo, for whom he played for in 2005 and 2007, and which was the last team for which he actively appeared as a player. He previously played for the Charlotte Rage (1993, 1995–96), Nashville Kats (1997–2001), Dallas Desperados (2002), Detroit Fury (2003–2004), Kansas City Brigade (2006), and Utah Blaze (2006). At the end of the 2006 season, he held several all-time AFL career records, including touchdown passes (767), passing yards (39,948), pass attempts (5,827), pass completions (3,621), and interceptions (155).
On December 6, 2007, Kelly was named the head coach of the proposed new All American Football League's Tennessee team. However, the league suspended operations March 12, 2008 (permanently, as things later developed, although only a delay was announced at the time), and Kelly signed with the Georgia Force two weeks later on March 26, 2008, but never actually participated in any games as an active player for the Force. Kelly retired as an Arena Football player following the 2008 season and currently serves as a commentator on Tennessee Volunteers football radio broadcasts.