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.
Right now I'm just happy to be back and get through this season and make sure I do my job. I've never had an issue with having to prove myself again and I'll try to do it again. We'll see where it takes me.
— Defenseman Torey Krug on signing with the Boston Bruins