The move comes just ahead of the NHL's trade deadline 3 p.m. ET on Wednesday, and on the heels of Calgary dealing captain Jarome Iginla to Pittsburgh last week.
The Flames get a conditional first-round draft pick, 22-year-old defenceman Mark Cundari and 26-year-old Swiss goaltender Reto Berra for Bouwmeester.
If the Blues don't make the post-season, Calgary gets a fourth-round pick in this year's draft and the first-round selection will be 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 defences 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."
For Iginla, Calgary picked up a first-round pick and two college forwards from the Penguins.
Bouwmeester was in the fourth year of a US$33.4-million, five-year contract he signed with the Flames in 2009.
He currently holds the consecutive games streak at 611, which remained intact because Bouwmeester was ineligible for the Blues' game Monday.
The departure of he and Iginla represents almost $14 million salary cap dollars off Calgary's payroll.
Calgary was 13-16-4 and 14th in the Western Conference heading into Monday's game versus the Oilers in Edmonton. The Flames announced the Bouwmeester deal prior to puck drop.
Facing a fourth straight season out of the playoffs, it appears general manager Jay Feaster has been given the green light from a Flames ownership to ship expensive veterans out of the lineup.
When he traded Iginla, Feaster said he didn't want to use the term "rebuild" but the Flames are clearly collecting draft picks and prospects with a view to becoming a playoff team in the future.
Bouwmeester, 29, has been a durable, big-minute man for Calgary, averaging just over 20 minutes per game this season. The Edmonton native has six goals and nine assists in 33 games.
The third overall pick in the 2002 draft by Florida, Bouwmeester quickly signed with Calgary when the Flames acquired his rights in 2009, rather than enter unrestricted free agency.
Bouwmeester has 71 goals and 229 assists in 750 NHL games, but has yet to appear in an NHL playoff game in his 10th season in the league.
Cundari, from Woodbridge, Ont., has seven goals and 18 assists for Peoria in the American Hockey League. The five-foot-10, 200-pound defender played four seasons with the Ontario Hockey League's Windsor Spitfires and won back-to-back Memorial Cups in 2009 and 2010. He went undrafted and signed with the Blues in 2010.
The Blues drafted Berra in the fourth round in 2006, but he has yet to play in the NHL. The 6-4, 200-pound goalie from Bulach, Switzerland, has a goals-against average of 3.01 and a save percentage of .906 in 49 games with Biel of the Swiss A League. He's played for Switzerland at the men's world championship.
The departure of Iginla and Bouwmeester fuels speculation that the Flames might also be shopping 36-year-old goaltender Miikka Kiprusoff around as well.
— With files from the Associated Press.
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