Brodziak, 32, could have been an unrestricted free agent July 1. He had seven goals and 11 points in 76 games in his first season in St. Louis after signing a one-year contract with the Blues on July 2, 2015.
Brodziak had two goals, including one game-winner, in 20 Stanley Cup Playoff games, helping the Blues reach the Western Conference Final, where they lost to the conference champion San Jose Sharks in six games.
The St. Paul, Alberta native was a seventh-round pick (No. 214) of the Edmonton Oilers at the 2003 NHL Draft. He has 105 goals and 239 points in 697 games with the Oilers, Minnesota Wild and Blues.