The Giants announced that Jennings died at his home in Upper Saddle River on Wednesday morning.
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.