Pierre LeBrun of The Athletic reports the deal is for five years and is worth around $25 million depending on bonuses.
McLellan began the 2018-19 season as bench boss of the Edmonton Oilers but was relieved of his duties on Nov. 20 after the team got off to a 9-10-1 record.
The 51-year-old enjoyed his greatest success in San Jose, coaching the Sharks to the playoffs in six of his seven seasons with the club, including back-to-back conference final appearances in 2010 and 2011.
McLellan has international experience on his resume as well, coaching the Canadian national team to a perfect 10-0 record and a gold medal at the 2015 World Championship.
The Kings fired John Stevens as head coach on Nov. 4 after a 4-8-1 start to the 2018-19 campaign and have had Willie Desjardins fill the role on an interim basis since.