In return, the Flames got a first-round pick and two prospects -- defenseman Mark Cundari and goaltender Reto Berra.
If St. Louis does not qualify for this year's playoffs, the Flames will receive St. Louis' fourth-round selection in this summer's draft, with the first-round pick being deferred to 2014.
"He's certainly a big body and he's a tremendous skater," Blues general manager Doug Armstrong said. "He's a workhorse back there and he logs 25 minutes a night on a regular basis. He gives us, really, what we believe is one of the stronger defenses in the NHL right now.
"When you bring Jay and (Jordan) Leopold into it with the consistent players we have on the right side, we have a lot of players now."
The move comes after Calgary started to rebuild by trading captain Jarome Iginla to Pittsburgh last week.
The NHL trade deadline is 3 p.m. on Wednesday.
Bouwmeester, who has an annual cap hit of $6.68 million through to the end of next season, has six goals and nine assists in 33 games in 2013.
Bouwmeester joined Calgary in 2009 after being drafted third overall by the Florida Panthers in 2002. He has 71 goals and 229 assists in 10 seasons with the Flames and Panthers.