Langer died at a hospital in Coon Rapids, Minnesota, according to his wife, Linda.
Langer was a six-time Pro Bowl selection who was elected to the Pro Football Hall of Fame in 1987. He is one of four Miami players to be elected in his first year of eligibility, along with Paul Warfield, Dan Marino and Jason Taylor, the Miami Herald reported.
Langer is the third member of the Dolphins' perfect season squad to die this year. Fellow Hall of Famer Nick Buoniconti, who was the anchor of Miami's defense, died July 13. Bob Kuechenberg, who lined up next to Langer at left guard, died in January.
Langer led Miami to three consecutive Super Bowls in the early 1970s, including 1972, when Miami went 17-0.
"I was saddened to hear of the passing of Jim. He was the rock in the middle of one of the greatest offensive lines in the history of the National Football League," former Miami wide receiver Nat Moore, who is now an executive with the Dolphins, told the Herald. "More than that, he was a leader of our team both on and off the field and set the standard for which all centers are measured. On behalf of the Dolphins and our alumni we send our thoughts and prayers to his family. He will be forever missed."
Langer played in Miami from 1970 through 1979 and played his final two seasons with the Minnesota Vikings.
"This is a tremendous loss," former teammate Dick Anderson told the Herald. "We were fortunate to have three of the best offense of lineman in the League with Jim, Kooch (Kuechenberg) and Larry Little. Jim was the center and leader in all ways both on and off the field. He was a remarkable individual and will be missed."