Salaam attended the University of Colorado, where he played for the Colorado Buffaloes football team from 1992 to 1994. As a junior in 1994, Salaam had one of the best individual seasons in college football history, rushing for a school-record 2,055 yards and becoming only the fourth college running back to run for more than 2,000 yards in a season. He also amassed 24 touchdowns and helped lead Colorado to an 11–1 record, including a 41–24 win over the Notre Dame Fighting Irish in the 1995 Fiesta Bowl, and a No. 3 finish in the final Associated Press Poll. The Buffaloes' only loss of the season was to the Big Eight Conference rival Nebraska Cornhuskers, which finished undefeated and ranked No. 1 in both the Associated Press and United Press International polls at season's end. Salaam had four consecutive 200-yard rushing games during the season, his best effort coming against the Texas Longhorns, when he set a school record with 362 yards total offense in a 34–31 Colorado win in Austin. He was a unanimous first-team All-American and became Colorado's first Heisman Trophy winner in December, besting running back Ki-Jana Carter of Penn State and quarterbacks Steve McNair of Alcorn St. and Kerry Collins of Penn State. Salaam decided to forgo his final season of college eligibility and entered the NFL Draft.
The Chicago Bears selected Salaam in the first round of the 1995 NFL Draft, and he played for the Bears from 1995 to 1997. As a rookie, he rushed for over 1,000 yards and scored 10 touchdowns. Problems with injuries, fumbles, and marijuana use led him to spend only three years with the Bears. During his two final years with Chicago, Salaam mustered only 608 combined yards. Salaam spent 1999 with the Cleveland Browns and the Green Bay Packers, but only played in two games for the Browns that year.
Salaam briefly played in the XFL for the Memphis Maniax, but injury cut his season short and the league folded after one season. He was the fourth-most prolific rusher in the league with 528 yards. After his stint with the Maniax, he tried out for the NFL's Detroit Lions, but did not make the team.
Salaam launched what appeared to be a final attempt at an NFL career in 2002, beginning with a much publicized training at the Cris Carter Speed School. He was picked up by the San Francisco 49ers in 2003 but in August 2003, Salaam was subsequently let go by the 49ers in the second-to-last round of cuts. Despite receiving accolades from then 49ers head coach Dennis Erickson, Salaam was never signed by another NFL team.