Brooks attended Detroit's Mackenzie High School where he played as a defensive lineman, before graduating in 1981. He accepted a scholarship to the University of Michigan, where as a freshman he was tried at outside linebacker.
As a sophomore he was moved to defensive tackle and started 7 games. He received All-Big Ten honors as a junior and senior. In 1984 at 6'6", 273 lbs., he led the team with 6 sacks and 13 tackles for loss, while cementing his place as one of the biggest and best defensive linemen in school history.
In the 1985 NFL Draft the Dallas Cowboys where targeting Jerry Rice with their first round selection, but drafted Brooks after Rice was taken by the San Francisco 49ers.
In 1987 he was named the starter at left defensive tackle and led the team's defensive linemen with 67 tackles, while adding 3 sacks. In 1988 he registered 71 tackles and five sacks.
In 1989 he clashed with new head coach Jimmy Johnson, before being traded along with a fourth round draft choice to the Denver Broncos, in exchange for a third round draft choice.