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 EightAthlete 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, 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.
Collegiate all-century teams
In 1999, Rimington was selected as the starting offensive center by Sports Illustrated in their "NCAA Football All-Century Team". The second and third team centers were Alex Wojciechowicz and Dwight Stephenson. Rimington is one of six Nebraska Cornhuskers on SI'sAll-Century Team 85 man roster; the others being Rodgers, Glover, Steinkuhler, Tommie Frazier and Aaron Taylor. In 1999, Rimington was selected as the starting offensive center to the Walter Camp Football FoundationAll Century Team. The other centers selected were Jim Ritcher, and Mel Hein,. Rimington is one of six Nebraska Cornhuskers on the Walter Camp 83 man roster; the others being Rodgers, Steinkuhler, Will Shields, Frazier and Taylor. Rimington is one of 54 players, one of five Cornhuskers, and the only center named to both the Sports Illustrated and Walter Camp All-Century teams.
Professional career
Rimington was selected in the first round of the 1983 NFL Draft by the Cincinnati Bengals. He played five seasons with the Bengals and two with the Philadelphia Eagles before retiring at the end of the 1989 NFL season.
Rimington Trophy
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.
Personal
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.