Bouwmeester, who is eligible to become an unrestricted free agent on Wednesday, was acquired by Calgary in a trade with the Florida Panthers as the NHL entry draft wrapped up Saturday with the final six rounds at Bell Centre.
Florida acquired Jordan Leopold -- also on the verge of free agency -- and a third-round pick (67th overall), which the Panthers used to draft right wing Josh Birkholz.
The trade gives Flames general manager Darryl Sutter a window of exclusivity in negotiating a new contract with Bouwmeester and his agent, Bryon Baltimore.
"I think we have everybody under contract that we want under contract, and we're trying to get him under contract," Sutter said.
Bouwmeester, among the most laidback players in the NHL, was even-keeled Saturday in an interview with ESPN.com.
"I was very aware of all the rumors, so to say it was a surprise, I'd be lying," Bouwmeester said after a round of golf with family. "I half-expected for something to happen."
He said he knew Sutter was on his way to see him sometime in the next few days.
"It'll be good to talk, so we'll see what happens," Bouwmeester said.
With just a few minor deals completed Saturday -- aside from the trade involving Bouwmeester -- Toronto general manager Brian Burke noted that it's difficult to find a trading partner willing to take on multiyear deals in the current economy.
"Right now, if you've got contracts of any term on them, it's really hard to move guys," Burke said. "I thought there'd be more activity, but I'm not quite sure why there wasn't."
"The test will be if they sign him," Burke said. "If they sign him, then it was a very successful gamble. I mean, this kid's a good player."
A 6-foot-4, 214-pound native of Edmonton, the 25-year-old Bouwmeester had spent his entire career with Florida, which drafted him third overall in 2002.
"I chatted a couple of times with his agent and at that point in time it was just clear that they really wanted to have the opportunity to exercise his free agency right," Panthers acting GM Randy Sexton said. "About 18 months ago they gave us a list of teams that they were interested in and Calgary was right at the very top. He's an Alberta boy and Darryl's an aggressive guy, he's clever, he's creative -- I think he'll find a way to get them."
Bouwmeester, who had 15 goals and 27 assists last season, never made a playoff appearance in six full seasons with the Panthers. He has 53 goals and 150 assists in 471 games.
"To be able to play with guys like Dion and Robyn for a long time, that to me is pretty significant," Sutter said.
Leopold, a 28-year-old who has been traded four times, also is eligible for free agency next week.
"I was sleeping when I got the news, so that's funny. It caught me off guard a little bit," Leopold told the Miami Herald by phone from Minnesota. "I'm just taking this in. I don't think I can make a fair assessment because I haven't talked to the team yet ... I'm sure when things are over with, my agent will meet with their staff and discuss some options. I have open ears. This is a new opportunity for me.''
Information from ESPN.com's Pierre LeBrun and The Associated Press was used in this report.