The 46-year-old has spent four years working for GM Doug Armstrong, but his contract ran out in June.
The NHL's all-time leader in goaltending wins has connections to two Eastern Conference teams: the New Jersey Devils, where he won three Stanley Cup championships, and the New York Islanders, who have longtime Devils GM Lou Lamoriello in charge of hockey operations.
Brodeur's 22-year career as a goalie will culminate in November when he is enshrined in the Hall of Fame. He is a four-time Vezina winner, five-time Jennings winner for allowing the fewest goals in a season, and he won two Olympic gold medals with Canada.
Brodeur won the Calder Trophy in the 1993-94 season and overall played 1,259 games over 21 seasons in New Jersey. Brodeur played seven games in his final season (2014-15) for the Blues.
Brodeur was the co-GM of Team Canada for the world championships last May.
The Blues promoted director of amateur scouting Bill Armstrong to assistant GM. He is not related to Doug Armstrong, who on Tuesday also named Kevin McDonald pro scout and GM of St. Louis' American Hockey League affiliate and Glen Wesley development coach.
Information from The Associated Press was used in this report.