Ware grew up in the Galveston, Texas region, hoping to play football at the University of Texas. He said "I was going to Texas. All they had to do was lie to me and tell me I was going to play quarterback once I got there. Thank goodness they told me the truth [that] they were going to move me to defense". After graduating from Dickinson High School, Ware instead played at the University of Houston, where he was the first black quarterback to win the Heisman Trophy in 1989, along with the Davey O'Brien Award, the latter award given to the most outstanding college quarterback of the year. That year, his junior year, he threw for 4,699 yards, 44 touchdowns, and set 26 NCAA records. Many of the records were thanks to the innovative use of the Run & Shoot offense, which his successor, David Klingler, also used to great effect. The Cougars ended the season ranked the #14 team in the nation by the Associated Press. He then declared for the NFL Draft, foregoing his senior year.
Ware joined the Lions for the 1990 season, teaming with the previous Heisman Trophy winner from 1988, Barry Sanders. Ware spent four years with Detroit, playing 14 games and starting six: then-coach Wayne Fontes insisted on starting the oft-injured Rodney Peete, and usually replacing Peete with Erik Kramer when Peete was hurt or played poorly. Fontes generally only played Ware when the Lions were out of the playoffs or already losing a game by a wide margin. Ware's best stretch came late in the 1992 season when the Lions were out of the playoffs: he won two of three games. The loss came on Monday Night Football to the San Francisco 49ers. He began 1994 on the roster of the Los Angeles Raiders, but was released after several games. In 1995 he was signed by the Jacksonville Jaguars, one of the NFL's two expansion teams that year. As a former Heisman Trophy winner, Ware's presence gathered much local excitement in Jacksonville, but ultimately, Ware was cut from the team the week before the regular season began.