The team issued a statement Monday saying that he "has left the team and been placed on unconditional waivers for the purpose of terminating his contract with the club."
The move comes a day after the 36-year-old received a $2.65 million roster bonus.
Kovalchuk had nine points in 17 games for the Kings this season, and Los Angeles is last in the Pacific Division.
He had returned to the NHL last season after a five-year hiatus in the KHL. The Kings gave him a three-year deal with a cap hit of $6.25 million, but the situation never really worked out. He had 16 goals and 34 points in 64 games last season.
Kovalchuk was a three-time All-Star in his previous stint in the league. He scored 40 or more goals six times.
Kovalchuk was the first overall pick in the 2001 draft. He signed a 15-year, $100 million deal with the Devils in 2010 but then retired from the NHL in 2013.