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 kept refreshing the page on the NHL website after the second round and I was shocked he lasted that long. I'm sure the Coyotes were pretty happy to get him. He's such a good player and he plays big in big games.
— Arizona Coyotes forward Henrik Samuelsson on prospect Edgars Kulda being draftedd