Gillies played 12 seasons with the Islanders, winning four consecutive Stanley Cups in the 1980s. He finished his career with a two-year stint in Buffalo, ultimately racking up 697 points in 958 games.
He had his No. 9 retired by the Islanders in 1996 and was inducted to the Hall of Fame in 2002.
"The entire Islanders community is devastated by the loss of Clark Gillies," Islanders general manager Lou Lamoriello said.
"He epitomized what it means to be a New York Islander. The pride he felt wearing the Islanders sweater on the ice was evident by his willingness to do anything to win. Off the ice, he was just as big of a presence, always taking the time to give back to the local community.
"The New York Islanders have four Stanley Cups because of the sacrifices he and the members of those dynasty teams made for the franchise. On behalf of the entire organization, we send our deepest condolences to the entire Gillies family."
NHL commissioner Gary Bettman released the following statement:
"The National Hockey League mourns the passing of Clark Gillies, a tower of strength on the ice for the dynastic New York Islanders of the early 1980s and a pillar of the Long Island community ever since. Gillies helped define the term "power forward" during a 14-season, Hall of Fame career with the Islanders and Buffalo Sabres that was highlighted by winning four Stanley Cups with the Islanders."
Gillies was one of 17 Islanders to win every championship between 1980 and 1983.