The NHL's Board of Governors was unanimous in its approval of the $130 million sale that also includes the Peoria Rivermen minor league team and "significant interest" in the Peabody Opera House.
Stillman, who has been a minority owner of the team since 2007, takes over from the Dave Checketts-led SCP Worldwide group that has owned the team since 2006.
Stillman is the eighth owner since the club was created in 1977. He also is chief executive officer of Summit Distributing, a St. Louis beer distributor.
Chicago-area businessman Matthew Hulsizer had led another group's bid to buy the team, but the NHL ended the arrangement in January over financial concerns.