Jennings, who played for Giants from 1973 to 1984 and holds the team record with 38,792 net punting yards, died after a 17-year battle with Parkinson's disease.
The four-time Pro Bowler is the Giants' all-time leader in punts with 931, far ahead of Sean Landeta, who punted 526 times for the Giants.
Jennings ended his career with the New York Jets, spending three seasons with the squad prior to his 1987 retirement.
He worked as a Jets radio commentator from 1988-2001, and then went behind the mic for the Giants from 2002-07, partnering in the broadcast booth with Bob Papa and the late Dick Lynch.
"Dave Jennings was one of the all-time great Giants," team President John Mara said in a statement. "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."
Jennings is survived by his sister Susan Jennings and her husband Harley.