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.
This is a great day for me. This is something I've been thinking about for a long time. This is a great opportunity that the St. Louis Blues organization, (owner) Tom Stillman and Doug Armstrong are giving me and trusting me in doing...This is going to be a great challenge for me.
— Martin Brodeur, after announcing his retirement as an NHL player and becoming a senior adviser with the Blues on Thursday