Burns battled cancer of the colon and the liver in 2004 and 2005 and hoped he had beaten the disease, but in January 2009 doctors found it had spread to his lungs.
"Just as they will remember Pat for his success as a coach, hockey fans also will remember his humor, his honesty, his humanity and his courage," NHL Commissioner Gary Bettman said in a statement. "As it mourns the loss of an outstanding contributor to the game, the National Hockey League sends heartfelt condolences to Pat's family and friends."
Burns became the Devils coach in 2002, leading the team to a 46-26-10 record and 108 points. New Jersey beat the Anaheim Mighty Ducks in seven games to win the franchise's third Stanley Cup title in his first season.
"On behalf of the ownership, management, staff, and players of the New Jersey Devils, we are all deeply saddened by the loss of Pat Burns," Devils President Lou Lamoriello said in a release. "Pat was a close friend to us all, while dedicating his life to his family and to the game of hockey. He has been part of our family here in New Jersey for eight years."
Burns also coached Boston, Toronto and Montreal, reaching the Stanley Cup finals with the Canadiens and twice leading the Bruins to the playoffs.
"Pat was a great coach and more importantly a wonderful man," Bruins President Cam Neely said. "The Bruins are honored to have him as a part of our history."
The Maple Leafs reached the conference finals in 1992 and 1993 under Burns.
"Pat forged a tremendous bond, not only with a very good veteran team in Toronto, but also with Leafs fans everywhere," Cliff Fletcher, the Maple Leafs' former general manager said in a statement. "He commanded respect from the players, and the team quickly had great success while taking on the identity of the head coach."
Burns was the first three-time winner of the Jack Adams Award as the NHL's top coach, receiving the honor with the Bruins, Maple Leafs and Canadiens. He is the only person to win it with three teams.
Burns had a career mark of 501-353-165 (.573) in 1,019 NHL games.
"I always tell everybody that he, more than any other coach that I ever played with, had a feel behind the bench that was better than most coaches," former Canadiens goalie Brian Hayward said. "He had a read on who was going well on any given night better than any other coach I ever had.
"I wouldn't describe him as a player's coach, because people naturally think that means that he's your friend - and he wasn't our friend. But we had a lot of respect for what he brought. He worked hard, but in many ways, he was more of a people person-type of coach than an Xs-and-Os type of coach."
Survivors include his wife, Line; daughter, Maureen; son, Jason; stepdaughter, Stephanie; and stepson, Maxime.
Funeral arrangements will be announced over the next few days.