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 winner of the Heisman Trophy in December, beating out running back Ki-Jana Carter of Penn State and quarterbacks Steve McNair of Alcorn State and Kerry Collins of Penn State. Salaam also won the Walter Camp Award and Doak Walker Award.

The Chicago Bears selected Salaam in the first round, with the 21st overall selection, of the 1995 NFL Draft. He played for the Bears from 1995 to 1997. As a rookie, he rushed for 1,074 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. The Bears traded Salaam to the Miami Dolphins before the 1998 season, but the trade was undone when Salaam failed a physical examination with Miami. 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 in 2001, but injury cut his season short and the league folded after one season. He finished the year with 528 yards gained.

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 signed by the Toronto Argonauts of the Canadian Football League (CFL) on February 20, 2004. He was then suspended by the Argos in May, effectively ending his career.

Salaam was found dead on December 5, 2016, in a park in Boulder, Colorado. An autopsy was performed due to the fact that authorities found a note near the body and were investigating it as a possible suicide.

Salaam’s family did not consent to neuropathological tests that would have revealed whether he had previously sustained chronic head trauma, such as chronic traumatic encephalopathy. They declined, due to religious reasons, to have his brain tested to determine whether his depression had been linked to such injuries from his days as a player. Salaam was Muslim and Islam prohibits bodies from being defiled after death.