Kelly grew up in the Pittsburgh suburb of East Brady, Pennsylvania. Kelly is generally considered one of the elite quarterbacks in the history of the National Football League.

Kelly was perhaps best known for running the Buffalo Bills' "No-Huddle Offense", which was a fast-paced offense that denied opposing defenses the opportunity to make timely substitutions. This led to mismatches and defensive communication breakdowns and, in the 1990s, established the Bills as one of the NFL's most successful and dangerous offenses.

Kelly helped lead the Bills to emergence as one of the NFL's greatest teams of the 1990s. Kelly's primary wide receiver with the Bills, Andre Reed, set numerous NFL records. Kelly's running back, Thurman Thomas, is a member of the Pro Football hall of Fame. Kelly played for Marv Levy.