The first game will be played during that season at Fenway Park, the home of the Red Sox who have a long rivalry with the New York Yankees of the American League. The second game will be in 1987 in New York.
Proceeds from the games will go to Boston's Jimmy Fund for cancer research and for amateur baseball in New York.
"We are pleased to start this rivalry with the Red Sox," Mets' General Manager Frank Cashen said. "The fans in both cities will get a chance to see stars they wouldn't normally."
"The Mets have some outstanding young stars and the series will allow our New England fans a chance to see them play," said Red Sox General Manager Lou Gorman. "The real winners will be the Jimmy Fund and amateur baseball in New York City."