Bourque is the 26-year-old son of Ray Bourque, the Hall of Fame defenceman who spent 21 seasons with the Bruins.
The deal was announced by Bruins general manager Peter Chiarelli on Saturday.
Bourque appeared in 73 games for Hershey of the AHL, and scored 27 goals. He was drafted 33rd overall by the Capitals in the 2004 NHL Entry Draft. In 2009-10, Bourque appeared in 20 games for the Pittsburgh Penguins.
I was going nuts and I saw [Subban], he was going crazy, and the ref had no idea where to go. [Subban] was skating to me, and I was skating to him and the ref was right in between us and I don't know, I kind of hit him pretty hard, I thought, but those were some emotions and I'm pretty sure he understands that.
— Montreal forward Alex Galchenyuk on the celebration following his OT goal against Ottawa in Game 2