He died peacefully in his sleep Monday, the organization said.
"We are heartbroken to share that our beloved husband and father has passed away," a family statement from wife, Nancy, and daughters, Sarah and Anne, said. "We send our love out to his fans, as we mourn his loss with you."
Seaver played 12 seasons with the Mets.
After years of being a league-wide joke for the franchise's hapless play since their inaugural season in 1962, Seaver and the team, which was dubbed the Miracle Mets, were able to overcome seasons of mediocrity and win the 1969 World Series.
He's credited with 311 game wins, 3,640 strikeouts and a 2.86 earned-run average during a career that started in 1967 and ended in 1986.
"Tom Seaver’s life exemplified greatness in the game, as well as integrity, character, and sportsmanship—the ideals of a Hall of Fame career,” said Hall of Fame chairman Jane Forbes Clark. "As a longtime member of the Hall of Fame Board of Directors, Tom brought dignity and wisdom to this institution that will be deeply missed."
He also played parts of six seasons with the Cincinnati Reds, parts of three with the Chicago White Sox, and one with the Boston Red Sox.
A version of this story originally appeared on NBCNews.com.