In exchange, the Flames sent defensemen Lawrence Nycholat and Ryan Wilson, along with a 2009 second-round draft pick.
Later on Wednesday, the Flames pulled off a second deal, acquiring center Olli Jokinen and a 2009 third-round draft choice from the Phoenix Coyotes in return for forwards Matthew Lombardi and Brandon Prust and a conditional 2009 first-round pick.
"We wanted to get a center and we wanted a defenseman, we knew we'd have to pay a price," Flames general manager Darryl Sutter said. "Being able to accomplish this today was important."
Leopold, 28, has played in all 64 games for the Avalanche this season, with six goals and 14 assists.
"Once I left Calgary a couple years ago, I know Darryl didn't really want to part ways, but it's the nature of the beast and it's the business," Leopold said. "I thought in the long run that maybe Darryl was thinking about me and apparently he was."
Jokinen, 30, has 21 goals and 21 assists in 57 games with the Coyotes this season, his first with the team. This is the fourth trade of his career; he also has played with the Los Angeles Kings, New York Islanders and Florida Panthers. The Coyotes acquired him on June 20, 2008.
"He's a big, first-line centerman who scores and plays tough. He can play against the big guys on the other team," Sutter said.
Jokinen told the Calgary Herald: "I don't think I've been playing on a level that I can play at. You don't want to be just average. You want to bring your best every day. That's what I want to do the rest of the year. It's a fresh start. It's like the season is going to start again.
"You want to fit in right away. You want to get to know the guys. It's a good feeling right now. It's a dream come true."
Nycholat, 29, was claimed off waivers Tuesday by the Flames from Vancouver. The journeyman has played 45 career games in the NHL, with the New York Rangers, Washington Capitals, Ottawa Senators and Canucks.
Wilson, 22, signed as an undrafted free agent on July 1, 2008, played all of this season with the Quad City Flames, Calgary's AHL affiliate.