Boston last won the cup in 2011, defeating the Vancouver Canucks in seven games but finished this season with the best record in the league on 117 points.
According to Bovada, the Bruins are 7/2 favorites to win the cup this summer with the St. Louis Blues at 6/1.
The Pittsburgh Penguins were defeated by the Bruins in last season's conference finals but they are the third favorite at 7/1.
Bettors can also get decent odds of a cup repeat, with last year's champion Chicago Blackhawks placed at 8/1.
The first round of the NHL playoffs will start on wednesday, with the Tampa Bay Lighting taking on the Montreal Canadiens and the Penguins facing off against the Columbus Blue Jackets.
In the Western Conference, the Anaheim Ducks will face the Dallas Stars.