The move comes ahead of the NHL's trade deadline of 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. For Iginla, Calgary picked up a first-round pick and two college forwards from the Penguins.
If the Blues don't make the post-season, Calgary gets a fourth-round pick in this year's draft from St. Louis and that first-round selection will be deferred to 2014.
"Our point is, if they make the playoffs, and we certainly hope that they do ... that's three first-round picks in the '13 draft," Feaster said in an interview with The Canadian Press.
"If they don't make it and we get it next year, that's back-to-back years where we would be going in with two first-round picks, which organizationally we think is really important."
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 NHL's consecutive games streak at 611, which remained intact.
His trade was announced after the puck dropped between St. Louis and Minnesota, which made Bouwmeester ineligible to play in that game, but before Calgary's game in Edmonton.
"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."
Calgary sits 13-17-4 and 14th in the Western Conference after Monday's 4-1 loss to Edmonton.
Facing a fourth straight season out of the playoffs, it appears Feaster has been given the green light from a Flames ownership to ship expensive veterans out of town. When he traded Iginla, Feaster said he didn't want to use term "rebuild" for the hockey club.
"I use the phrase 'retool' and I realize people have said 'Feaster can call it anything he wants, but we're going to call it what we think it is,' and that's fine, that's fair if that's what people want to do," Feaster said.
"The reality of it is while two really good players went out the door, this franchise has missed the playoffs with those two really good players the last three years. At the time we initiated both transactions, we were in hard to try and make the playoffs this year. It's time for us to go in a new direction."
The departure of Bouwmeester and Iginla also represents almost $14 million in salary cap dollars coming off Calgary's payroll.
"The salary cap comes down in the National Hockey League next year and there are going to be teams that are in trouble," Feaster said. "There are going to be teams that need to move players because they don't have the cap space. We're going to be a team that's sitting there with cap space. We're going to have an opportunity to get better quickly."
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.
"The position we are in, we knew changes were going to happen," said defenceman Mark Giordano after the Flames lost 4-1 to the Edmonton Oilers later Monday. "It's tough to see a good buddy and teammate go to another team. It's tough to see guys go."
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 before signing with the Blues in 2010.
"He's a physical guy, in-your-face guy," Feaster said. "Our players in Abbotsford hate playing against him because he's just relentless. He's hard to play against. He's not a big guy, but he plays a bigger man's game. We don't have that kind of a physical guy and certainly at that age.
"We're aware of the fact he has a wrist injury that's been bothering him and he's probably going to be on the shelf for about seven to 10 days."
The Blues drafted Berra in the fourth round in 2006, but he has yet to play in the NHL.
The six-foot-four, 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 also played for Switzerland at the world hockey championship.
The Flames acquired the rights to Finnish goaltender Karri Ramo in the same deal that brought Mike Cammalleri to Calgary in January 2012. Feaster says his scouts identified Ramo, currently playing in the KHL, and Berra as the top two goaltenders in the world not playing in the NHL.
"Recognizing that at some point in time we're going to face life without Miikka Kiprusoff, to have both of those guys in our organization and be in a position where we can try to sign them, that was a big piece of it too," Feaster said of his latest transaction.
That's as much Feaster would say about Kiprusoff, a 36-year-old goaltender with a year remaining on his contract. The departure of Iginla and Bouwmeester fuelled speculation that the Flames are also shopping the Finn, who gave up three goals on six shots before getting pulled in Monday's loss to the Oilers.
"We've been pretty steadfast in saying we're not going to discuss trade issues or trade-deadline matters until such time as we have something to say," Feaster said. "Until such time we have anything to announce on any of the guys, we're not talking."
— With files from Shane Jones in Edmonton and the Associated Press.Suggest a correction