Rimington attended the University of Nebraska where he was a consensus First-Team All-America in 1981 and 1982. In 1981, he was named the UPIBig 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, the UPI National Lineman of the year, and an NCAATop Five winner.
Rimington won the Outland Trophy, given to the nation's top interior offensive or defensive lineman, in 1981 and 1982, and is its only two-time winner. 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. He is one of eight Nebraska Cornhusker players to win the Outland Trophy and one of five Nebraska winners of the Lombardi Award. Nebraska players have won nine Outland Trophies overall, by far the most in the nation. Oklahoma has the second most with four. Rimington, along with fellow Cornhuskers Rich Glover, Dean Steinkuhler and Ndamukong Suh, won both the Outland Trophy and Lombardi Awards. Only thirteen players in NCAA history have won both of these prestigious awards.
Rimington's #50 jersey was retired by the team in 1982, one of only sixteen Cornhuskers ever so honored. In 1994 he was named to the FWAA1969-1994 All-America Team, one of just twenty-five athletes and one of three Cornhuskers named to that team, along with Steinkuhler and Johnny Rodgers. In 1997, he was inducted into the College Football Hall of Fame. In 1999 he was selected to the Nebraska All-Century Football Team via fan poll 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. In 2008, he was named to the Orange Bowl's 75th Anniversary All-Time Team.
Rimington was a first-team academic All-American in 1981 and 1982. In 2004, Rimington was inducted into the CoSIDA Academic All-America Hall of Fame. Other Class of 2004 inductees were: Terry Hoage, Georgia '84, Rolf Benirschke, UC Davis '77*, Dylann Duncan Ceriani, Brigham Young '88 and Gill Beck, Appalachian State '78. He is one of three Huskers to have been inducted into the CoSIDA Academic All-America Hall of Fame, the others being 2008 inductee Karen Jennings '93 and 2009 inductee Pat Tyrance '90.
The Rimington Trophy is named in his honor and since 2000 has been given annually to the nation's top collegiate center. Since 2003, a Rimington Trophy has been awarded to the top center in each division of college football. The sculptor of the Rimington Trophy is Marc Mellon, who is also the sculptor of the NBA MVP Trophy.
Following his professional career, Rimington has served with the Boomer Esiason Foundation in their fight against cystic fibrosis. He has been with the foundation since 1993 and has been president since 1995. Rimington is a member of Lambda Chi Alpha.