King finished last season as Chicago's interim coach after Jeremy Colliton was fired on Nov. 6. He was in the mix for the full-time job, but Richardson was hired last month.
King, 55, went 27-33-10 with the Blackhawks, drawing praise from general manager Kyle Davidson for his work during a challenging period for the rebuilding franchise. The former NHL forward coached the team's AHL affiliate in Rockford before taking on the interim role.
Kevin Dean also was hired as an assistant on Monday. Dean, 53, was an assistant with the Boston Bruins for the previous five seasons. Dean was an NHL defenseman for seven seasons, finishing his playing career with 96 games with the Blackhawks.
Goaltending coach Jimmy Waite and video coach Matt Meacham also are returning to Chicago's staff.
"It's great to have this experienced staff with me behind the bench," Richardson said in a release. "Derek has made an impact here on this organization and I'm thrilled to have someone like him on our staff. Kevin's mind for the game and defensive focus will be an asset for us. It's great to have the cornerstone of this coaching group finalized and we will continue to add a few pieces."