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.
We think that Randy is a very good coach. Our players think that Randy is a very good coach. We think that he's going to get the most out of this group. With the addition of the two assistants, a bit of a different dynamic, we're very comfortable that this is a quality coaching staff that's going to maximize the potential of this team.
— Maple Leafs GM Dave Nonis on head coach Randy Carlyle and his staff