TSN's Darren Dreger reported Muller, who was fired last week as coach of the Carolina Hurricanes, will receive a two-year contract to join veteran Blues coach Ken Hitchcock.
"We are excited to add Kirk to our staff," general manager Doug Armstrong said. "He was a Stanley Cup-winning player, and as a coach has shown excellent communication skills and the ability to relate to both young and veteran players."
Muller won the Stanley Cup with the Montreal Canadiens in 1993 and returned to the Final in 2000 with the Dallas Stars, coached by Hitchcock. Armstrong was promoted from assistant general manager to GM during Muller's tenure with the Stars.
"Once I talked to Doug, I really didn't pursue anything else," Muller told the St. Louis Post-Dispatch. "After that, I just sat down and knew right away that if it works out on their part, it's just a great fit.
"I'm familiar with [Armstrong and Hitchcock] from the Dallas days. Hitch coached me, Doug was the GM when I was playing. I just know that they're hard-working guys and the team really patterns off their work habits. I love the style and the type of team they've put together. I just thought they were guys I'm familiar with and can continue to learn a lot from and kind of just grow together."
Muller, 48, was 80-80-27 during three seasons in Carolina. He was an assistant coach with the Canadiens from 2006-11.