St. Louis made the deal Monday because it has needed a center since Andy McDonald broke his left leg on Nov. 16. Steen has two goals and two assists in 20 games this season, and has 50 goals and 76 assists in 253 career games.
"We felt that we were acquiring a top-six forward who can contribute offensively and also play on our power play," Leafs general manager Cliff Fletcher told ESPN.com. "He's young, he's 25, and fits into the mold of what we're trying to do for the future."
Colaiacovo has an assist and six penalty minutes in 10 games this season. In 111 career games, he has 12 goals and 21 assists, and 57 penalty minutes.
Stempniak has three goals and 10 assists. In 233 career games, he has 57 goals and 73 assists.
Both Steen and Colaiacovo were first-round draft picks by Toronto.
The Leafs had extra bodies on the blue line, which made it easier to move the oft-injured Colaiacovo.
"We had nine defensemen here, so it was a deal we could afford to make," Fletcher said. "And hopefully it helps both teams."
The injury-riddled Blues acquired some much-needed depth with the deal.
"That's part of it," Blues president John Davidson told ESPN.com. "But it's more big-picture, too. Lee's a good person and a good player. But we've got [rookie] T.J. Oshie and when he comes back from injury will get more ice time.
"And we need someone back on the blue line that could move the puck a little better. The reports on Colaiacovo are that there's been injury problems but if he's healthy he's a pretty good player. So we have to take a chance at that."
The Blues have been hammered by injuries this season. Second-year defenseman Erik Johnson is out for the season, while forwards Oshie, Andy McDonald, Paul Kariya, Dan Hinote and Patrik Berglund are also injured.
"We're going to look for two guys that want a fresh start, and they're both getting it here," Davidson said.
Information from The Associated Press and ESPN.com's Pierre LeBrun was used in this report.