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 don't know how he does it. I don't know how he gets his body parallel with the player and pulls it through his legs like that. I know he's tried it a couple times in practice and it's never worked, so how he does it in a game, it's incredible.
— Capitals defenseman Mike Green on teammate Alex Ovechkin's highlight-reel goal against the Devils on Saturday