Goaltending coach Jim Corsi also was fired. Assistant general manager Martin Brodeur and goalie development coach Ty Conklin would fill that role for the remainder of the season.
Yeo's first game will be against the Toronto Maple Leafs at Scottrade Center on Thursday (9 p.m. ET; FS-MW, TSN4, NHL.TV).
Hitchcock was 248-124-41 in six seasons with the Blues, and 20-27 in the Stanley Cup Playoffs. The Blues finished first or second in the Central Division in each of Hitchcock's four full seasons. They lost 5-3 to the Winnipeg Jets on Tuesday and are fourth in the division with 53 points (24-21-5) this season.
After coaching the Blues to the Western Conference Final last season, Hitchcock signed a one-year contract on May 31 and announced this season would be his last. Yeo was hired as associate coach on June 13 and was scheduled to replace Hitchcock for the 2017-18 season.
Hitchcock, 65, is 781-473-111 with 88 ties in 20 seasons with the Dallas Stars, Philadelphia Flyers, Columbus Blue Jackets and Blues. He's fourth in NHL coaching victories, behind Scotty Bowman (1,244), Joel Quenneville (831) and Al Arbour (782). His 1,453 games coached are fifth.
Hitchcock won the Stanley Cup as coach of the Stars in 1999 and made the Cup Final in 2000, losing to the New Jersey Devils in six games. His teams have made the playoffs 13 times in 14 full seasons.
"He's a Hall of Fame coach, he's one of my best friends," Armstrong said. "But things change in sports.
"I talked to him last night after the game. It's really hard. Ken's probably my best friend. Ken and I talked a lot during the Christmas break and I just felt that ... you want to extend every last breath into making it work. We just haven't played well enough. At the end of the day, we were winning games and we'd look like a really good team, but part of what we've done now is ... I'm not sure if I'm going to make a lot of sense right now, but we don't lose with pride. It just felt like we were hit and miss, night in and night out. I think we need to demand more of ourselves. Our record is not indicative of what we thought [we'd have]."