Burns died of lung cancer at age 58 in Sherbrooke, Quebec, the team said.
Burns had an NHL coaching record of 501-353 with 151 ties.
"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," General Manager Lou Lamoriello said. "Pat was a close friend to us all. Today, the hockey world has lost a great friend and ambassador."
Burns began his NHL coaching career with Montreal in 1988 and in his first year led the Canadiens to the Stanley Cup Finals, where they lost to Calgary in six games. That year he won his first Jack Adams Trophy as the NHL's top coach.
After being dismissed by Montreal, he was hired by Toronto before the 1992-93 season. The Maple Leafs reached the conference finals in each of his first two years with the team and he earned his second Adams Trophy in 1993.
Burns later spent more than three years with Boston and won coach-of-the-year honors for the third time for leading the Bruins from last place to a playoff spot.
He then guided New Jersey to a Stanley Cup in his first year with the Devils in 2003 before being diagnosed with cancer the following season.