Rimington attended the
University of Nebraska–Lincoln, where he was a consensus First-team
All-American in 1981 and 1982. In 1981, he was named the
UPI Big Eight Player-of-the-Year and the
AP Big Eight Offensive Player of the Year, the only time in Big Eight Conference history that a
lineman was so honored. In 1982, he was the Big Eight (all sports) Athlete of the Year and UPI National Lineman of the year. In 1983 he was an
NCAA Top Five winner. Rimington won the
Outland Trophy, given to the nation's top interior offensive or defensive lineman, in 1981 and 1982 and is the only two-time winner of the award. He also won the
Lombardi Award in 1982, and placed fifth in the balloting for the
Heisman Trophy that same year. He and
Orlando Pace are the only three-time winners in the Outland/Lombardi category. Rimington is one of only thirteen players in NCAA history have won both of these awards. Rimington's #50 jersey was retired by Nebraska in 1982. In 1994, he was named to the
FWAA 1969-1994 All-America Team, one of just twenty-five athletes named to that team. He was inducted into the
College Football Hall of Fame in 1997. He was selected to the Nebraska All-Century Football Team via fan poll in 1999, and named to the All-Century Nebraska football team by
Gannett News Service. In 2002, he was named to the Athlon Sports Nebraska All-Time Team. He was named to the
Orange Bowl's 75th Anniversary All-Time Team in 2008. Rimington was a first-team academic All-American in 1981 and 1982.{{cite web |url=https://academicallamerica.com/documents/2016/10/13//1981%20FOOTBALL.pdf?id=1978 ==Collegiate all-century teams==