The 55-year-old Canadian, who guided Boston to an NHL record for wins and points in a season but never got past the second round of the playoffs, replaced Drew Bannister, who was fired after a 9-12-1 start by the Blues this season.
An 8-9-3 start this season by the Bruins led to Montgomery's firing, but he signed a five-year contract with the Blues.
"This was more an opportunity to get someone of Jim's caliber more than anything else," Blues president of hockey operations Doug Armstrong said.
"We've had to deal with our situations off the ice with injuries and everyone deals with that, but this decision was based 100% on having someone of Jim's caliber becoming available when I didn't know that was going to happen."
Montgomery is 180-84-33 as an NHL coach, having guided Dallas for two seasons and Boston for just over two campaigns, going 120-41-23 with the Bruins.
In the 2022-23 season, the Bruins won an NHL record 65 games and compiled a record 135 points under Montgomery, who was named the NHL's Coach of the Year, but were upset by Florida in the first round of the playoffs.
Boston also lost to the eventual 2024 Stanley Cup champions in last year's playoffs.
Montgomery was dropped by the Bruins last Tuesday and replaced by Joe Sacco.
"He certainly has a very positive demeanour, works well with the top players in the organizations that he's been with," Armstrong said. "He has a wealth of experience and he's at the prime of his coaching career."
The Blues, who won the 2019 Stanley Cup, have missed the playoffs the past two seasons.
Bannister went 39-31-6 as the Blues coach after replacing Craig Berube last December.
Montgomery gets his first test with the Blues on Monday when they visit the New York Rangers.
