The Giants announced that Jennings died at his home in Upper Saddle River on Wednesday morning after being informed of his death by his sister, Susan Jennings, and several close friends.
The most prolific punter in franchise history, Jennings had battled Parkinson's disease, a chronic degenerative neurological disorder, since 1996.
Jennings played for the Giants from 1974-84. He holds the franchise records for punts (931, or 405 more than second-place Sean Landeta) and yards (38,792). Jennings was selected to play in the Pro Bowl in 1978, '79, '80 and '82. He punted a career-high 104 times in 1979, which was the Giants record until Brad Maynard had 111 punts in 1997.
Jennings punted for more than 4,000 yards in a season three times (1979-81) and had a career-best 44.8-yard average in 1980
"Dave Jennings was one of the all-time great Giants," John Mara, the Giants president, said. "He was a valued member of the Giants family for more than 30 years as a player and a broadcaster, and we were thrilled to include him in our Ring of Honor."
Giants chairman Steve Tisch said Jennings lived his life with class and dignity, and he was the ultimate professional as a player and commentator.
"Dave is and always will be a Giants' Giant," Tisch said.
Hall of Fame linebacker Harry Carson said Jennings the first player he met joining the team in 1976, describing him as a great guy who was loved by everyone.
"The Giants were not very good when Dave and I were teammates in the 1970s," Carson said.
After leaving the Giants, Jennings punted for the Jets from 1985-87. He worked as a radio commentator for Jets games from 1988-2001.
In 2002, Jennings moved into the Giants radio booth with Bob Papa and the late Dick Lynch. He was also a part of the Giants pre and postgame shows. Jennings was replaced in the booth by Carl Banks after the 2007 season and left broadcasting the following year.
"Dave was always a guy that I admired from afar, and when we had an opportunity to add him to the Giants' broadcast team - when John Mara brought him back to the Giants family - it was a treat to work with Dave," Papa said. "He was meticulous in his preparation and Dave was a leader in rules interpretations. Dave knew all the rules. Whenever something came up, you could always turn to Dave and you knew he would get the rule correct and that was going to serve the audience best."
Jennings was part of the Giants' second Ring of Honor class in 2011. He joined the ring with running back Alex Webster, tight end Mark Bavaro and linebackers Brad Van Pelt and Banks.
Jennings did not play football at Garden City High School on Long Island. Jennings attended St. Lawrence University, winning two letters in basketball and earning the punter's job as a walk-on.
Besides his sister, Jennings is survived by her husband, Harley. The family has asked that donations be made in Dave's memory to the Michael J. Fox Foundation (www.michaeljfox.org).