The Dolphins confirmed the death of Mandich, who was also a star at Michigan. He was diagnosed with bile-duct cancer in early 2010, but continued to work on game broadcasts last season.
Mandich was a tight end for the Dolphins when they achieved the NFL's only perfect season in 1972, and he helped them repeat as Super Bowl champions the following year.
Besides working as a color commentator for most of the past 20 seasons, Mandich hosted a radio call-in show and luncheons for the Dolphins Touchdown Club.
"I was sad to hear about Jim's passing," said Hall of Fame head coach Don Shula, who coached Mandich in 1970-1977. "I always looked at him as a guy who was bright, well prepared and competitive. He was someone who I could count on as a player and was instrumental in the success we had during his time with the Dolphins."
Mandich won a wide following for his unabashed support for the home team and his signature call "All right, Miami!" But he was also candid in his criticism, such as when Bill Parcells gave up control of football operations before last season.
"He was a hired gun. He was a personality," Mandich said. "He came in; he leaves two years later. I feel like taking Listerine and washing my mouth out, because it doesn't feel good to me."
Before being drafted in Shula's first year with the Dolphins in 1970, Mandich was a Michigan captain in 1969, leading the Wolverines to a Big Ten co-championship and an appearance in the Rose Bowl. He was a first-team All-American and was inducted into the College Football Hall of Fame in 2004.
"I've played in a perfect season and in Super Bowls," Mandich said in 2008. "But I'm proudest of playing for the maize and blue."
Mandich played for the Dolphins until 1977, then spent one season with Pittsburgh before retiring. He had 121 career receptions, including 23 for touchdowns.
Funeral arrangements had not been announced.