His son-in-law, John Havens, said Doubleday died of pneumonia at his home in Locust Valley, N.Y., on Wednesday.
Doubleday was the grandson of Frank Nelson Doubleday, who founded the publishing company in 1896, and a descendent of Abner Doubleday, the mythical inventor of baseball.
After taking over the company from his father, Nelson Doubleday partnered with Fred Wilpon to become a majority owner of the last-place Mets in 1980.
Doubleday hired general manager Frank Cashen, who was the architect of the 1986 team that beat the Boston Red Sox in seven games.
The series is most famously known for Bill Buckner's critical error at first base. He let Mookie Wilson's slow grounder go through his legs, and the Mets capped a two-out rally in Game 6 with a 6-5 victory in the 10th inning at Shea Stadium.
The Mets went on to win Game 7.
"His life is to be celebrated. He was a wonderful man. He had a wonderful life," former Mets star Keith Hernandez said of Doubleday on the team's SNY broadcast Wednesday night.
Doubleday & Co. bought the Mets from the family of founding owner Joan Payson for $21.1 million, with the company owning 95 percent of the team and Wilpon owning 5 percent.
When Doubleday & Co. was sold in 1986, the publisher sold its shares of the team for $80.75 million to Wilpon and Nelson Doubleday, who became 50-50 owners.
Wilpon bought out Doubleday in 2002 in an acrimonious split. They fought over the valuation of the team.
Wilpon and his family bought Doubleday's 50 percent after the team was appraised at $391 million. Last spring, Forbes estimated the Mets were worth $858 million, third in baseball behind the New York Yankees ($1.6 billion) and the Boston Red Sox ($870 million).
The Mets released a statement saying, "Nelson had a love of baseball and the Mets" and they were saddened to hear the news of his death.
Ex-pitcher Ron Darling, also a Mets broadcaster, said: "It's a big loss for Keith and I. A guy that we looked up to."