Van Pelt was found dead Tuesday by his fiancee at his home in Harrison, Mich. He died from an apparent heart attack, the Giants said.
Van Pelt's only winning season with the Giants came in 1981, when Lawrence Taylor was drafted and the team made the playoffs for the first time in 18 seasons. Van Pelt played strong side linebacker with Taylor on the weak side and Harry Carson and Brian Kelley in the middle of a group called the "Crunch Bunch."
Van Pelt, who was 6 feet 5 and 235 pounds in his playing days, left the Giants in 1983 and spent two seasons with the Los Angeles Raiders before finishing his career with Cleveland in 1986. He played in 184 regular-season games and had 20 interceptions and 24 1/2 sacks.
"Brad was a very good friend," said Carson, who like Taylor is a member of the Pro Football Hall of Fame. "Obviously he was a great teammate, but I consider him more of a very good friend and very much like a brother. Having played together for a number of years . . . but then the relationship after football and the things that we did as a group of linebackers after football, those things really bonded us together."
Born April 5, 1951, in Owosso, Mich., Van Pelt was a star player on his high school football, baseball and basketball teams. At Michigan State, he played baseball as well as football and was drafted by the St. Louis Cardinals as a pitcher. He lasted into the second round of the NFL draft because many teams thought he would play baseball. He was an All-American safety in 1972, and became the first defensive player to win the Maxwell Award as the nation's top college football player.
Van Pelt was inducted into the Michigan State Athletics Hall of Fame in 2000 and the College Football Hall of Fame the next year.
He returned to Michigan State in the late 1990s and earned his bachelor's degree in health and physical education.
Van Pelt's son Bradlee spent three seasons as a backup quarterback in the NFL with Denver and Houston.
In addition to Bradlee, survivors include two other sons. Another son, Justin, died of an accidental overdose of painkillers and alcohol in 2001.