The Flames also got a seventh-round draft pick in the deal that sent defenceman Andre Zyuzin and prospect Steve Marr to the Blackhawks, who unloaded the $8-million US salary left on the final two years of Aucoin's contract.
The Flames needed a top-four defenceman because Calgary is expected to lose both Brad Stuart and Roman Hamrlik to unrestricted free agency on July 1.
"I'd rather have a player under contract than trying to negotiate a contract when you don't know what the marketplace is," said Flames GM Darryl Sutter. "I don't think we're a team that's going to free-agent shop for a high-priced defenceman because we don't have to."
The Flames went into the first round of the draft Friday with the No. 18 pick, but then had no more picks until the fifth round.
Sutter dealt No. 18 to St. Louis and dropped to 24th to pick up a third-round selection.
Calgary then chose Swedish centre Mikael Backlund in the first round.
The six-foot-four, 192-pound forward injured his knee last summer overtraining and played through the pain until December, when he had surgery. Backlund missed two months of the season, but was back playing with Vasteras in February.
He had 20 goals and 21 assists in 41 games.
Backlund was the leading scorer at the world under-18 championship in April with seven goals, including a hat trick against Canada, to help Sweden to a bronze medal.
"I'm a two-way playmaking centre who scores some goals and gets some assists," Backlund said. "I love to do that."
Aucoin, who was Chicago's captain last season, agreed to waive the no-trade clause in his contract.
"We're in a rebuilding phase here and this was a chance to go to a contending team," said Aucoin. "I've always like the way Calgary played and to play with a guy like Iginla is a once-in-a-lifetime opportunity."
The 33-year-old from Ottawa will start his 11th NHL season with the Flames. He had four goals, 12 assists and 50 penalty minutes in 59 games for the Blackhawks last season.
Aucoin, six foot two and 214 pounds, has also played for the Islanders, Tampa Bay and Vancouver, who drafted him in the fifth round of the 1992 draft.
He played for Mike Keenan, hired last week as the Flames' new head coach, for two seasons in Vancouver.
"I think he brings an ingredient for our power play without question," Keenan said. "He has an exceptionally hard shot. He's a right-handed shot, which I think is good for this hockey team.
"He's got some experience and he's a man that can take a lot of minutes and a lot of ice time."
Calgary's top two defenceman under contract, Dion Phaneuf and Robyn Regehr, are both left-handed shots.
Aucoin says he's looking forward to playing for Keenan again.
"He's a tough customer who demands from a lot from his players and the strong ones usually stick around," he said.