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.
For us it's a little bit different. I've never been in front of this much media. This is more than we've ever had to deal with in Tampa. I guess we're on a little bit bigger stage now. It's nice, you have to enjoy it. This doesn't happen too often.
— Lightning forward J.T. Brown after his first Media Day experience on Tuesday in preparation of Game 1 on Wednesday