General manager Rob Blake said a release announcing the news would come later Sunday, per Jon Rosen of Fox Sports West.
Stevens, 50, was the Philadelphia Flyers' head coach from 2006 to 2010. He was also the Kings' interim head coach for four games during the 2011-12 season, when they won their first Stanley Cup.
The Kings went 39-35-8 this season under Darryl Sutter, who was fired after a six-year run in Los Angeles. Sutter won two Stanley Cups and made the playoffs four times but missed the postseason in two of the last three years.
That led to sweeping change, with Blake replacing Dean Lombardi as general manager and now Stevens taking over as head coach. Also, former Kings star Luc Robitaille was named team president on April 10.
"You're looking at a heck of a core," Blake told reporters then of Jeff Carter, Anze Kopitar and Drew Doughty. "The three of them won two Stanley Cups. Throw Jonathan Quick into the mix, and that's a core you want to have around. To see those three sitting here, anybody would build a team around that."
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