Laura Prewitt, executive director of the Breeders' Cup Festival in Lexington, Ky., announced the death, saying Arnsparger died at his home in Athens, Ala.
The Miami team that won the Super Bowl in January 1973 had the only perfect season in NFL history. Arnsparger left the Dolphins after the 1974 Super Bowl to coach the New York Giants, going 7-28 before he was fired after an 0-7 start in 1976. He returned to Don Shula's Miami staff and remained with the Dolphins until 1983, helping them reach another Super Bowl.
"I was saddened to learn of the passing of Bill Arnsparger, who I thought was one of the greatest defensive coaches in football," Shula said in a statement. "He molded two championship units, the `No-Names' and the `Killer B's,' and was innovative in the way he used personnel.
"He pioneered situational substitutions with the `53' defense that changed the way the game was played on that side of the ball. If there was a Hall of Fame for assistant coaches, he would be one of the very first inductees. Mary Anne and I want to extend our condolences to ... the entire family."
Arnsparger was LSU's head coach from 1984-86, leading the Tigers to two Southeastern Conference titles in three season before leaving to become Florida's athletic director. He completed his coaching career as the San Diego Chargers' defensive coordinator in 1992-94.
Before jumping to the NFL with Shula with the Baltimore Colts in 1964, Arnsparger was a college assistant at Miami of Ohio, his alma mater, and Ohio State, Kentucky and Tulane. With the Colts, Arnsparger coached the defensive line on teams that reached the 1964 NFL title game and 1969 Super Bowl.
"Bill Arnsparger was a seminal figure in Dolphins history," the Dolphins said in a statement. "Along with Coach Shula and so many other great players and coaches, Bill played a pivotal role in establishing the Dolphins as one of the winningest teams in football and flagship franchises in professional sports. Our hearts and prayers go out to his loved ones and friends during this difficult time."
Arnsparger served in the Marines during World War II before attending college.
Funeral services will be held in his hometown of Paris, Ky., where he was born in 1926.