Morris played college football at the University of Michigan from 1984 to 1987 and broke the school's all-time rushing records in yards gained in a season (1,703 yards) and a career (4,392 yards). Though those records were broken 13 years later by Anthony Thomas, Morris still holds the U-M school record for all-purpose yards with 6,201. Morris was also the only player in Michigan history to lead the Wolverines in rushing for four years until Mike Hart did so from 2004–2007. In addition to his rushing yards, he had 99 receptions for 756 yards and 51 kickoff returns for 1,027 yards. He ranks fourth in U-M history in kickoff return yards. He also still ranks third in U-M history in rushing yards in a season and career. Morris was setting Michigan records during the same years Lorenzo White, the Big Ten's first 2,000-yard rusher, was totaling 4,887 yards for the Michigan State Spartans. Neither reached Archie Griffin's 5,589 yard total. Morris was a very versatile running back who was the first Michigan back to total over 30 receptions in a season and remains the only back to have done so twice. He continues to hold the career receptions record for running backs with 99.