The school said he died at his home in Newport Beach, California, after a two-year struggle with cancer.
Donahue has the most wins (98) of any coach in Pac-12 history and also the most victories (151) in UCLA history. He coached the Bruins from 1971 to 1975, working as an assistant under Pepper Rodgers and then Dick Vermeil, before taking over as head coach at age 31 and serving from 1976 to 1995. His first job out of college was as an assistant to Rodgers at Kansas for one season.
Donahue was the first to appear in a Rose Bowl game as a player, assistant coach and head coach. The Bruins won the New Year's Day game in 1983, 1984 and 1986 during his coaching tenure. He was the first college coach to earn bowl game victories in seven consecutive seasons, from 1983 to 1989.
Born in Los Angeles, Terrence Michael Donahue graduated from Notre Dame High in Sherman Oaks, California, before going to UCLA. He joined the football team as a walk-on defensive lineman in 1965. He helped lead the Bruins to their first-ever Rose Bowl win in 1966 with an upset of previously undefeated and top-ranked Michigan State.
He had a 151-74-8 coaching record at UCLA and a 98-51-5 mark in Pac-12 play. The Bruins won or shared five league titles during Donahue's tenure. He coached such future Hall of Famers as quarterback Troy Aikman, safety Kenny Easley and offensive tackle Jonathan Ogden.
Donahue was inducted into the College Football Hall of Fame in 2000. He joined the Rose Bowl Hall of Fame in 1997, and the press box at the Rose Bowl was named for him in 2013.
"He epitomizes everything you strive to be as a coach and as a human being," current UCLA football coach Chip Kelly said. "Since the moment I stepped on campus, he's been an incredible mentor and one of the most authentic, humble and toughest men I've ever met. He loved UCLA with all he had, and I can't express how important his guidance and friendship has been for me."
After retiring from coaching, Donahue worked for CBS, Fox and the NFL Network calling games.
He served as the 49ers' director of player personnel in 1999 and 2000 and as the team's general manager from 2001 to 2005.
Donahue turned down a chance to coach the Dallas Cowboys, a move that would have reunited him with Aikman in 1998.
He is survived by Andrea, his wife of 52 years; daughters Nicole, Michele and Jennifer; and 10 grandchildren.