According to TSN's Bob McKenzie, the deal is worth $6.25 million per season.
With regard to the signing, Kings general manager Rob Blake said, "We are excited to add Ilya to the L.A. Kings organization. He gives us an added element of skill and scoring along with a desire to win. We will withhold further comment until July 1."
July 1 marks the official opening of NHL free agency.
The 35-year-old Kovalchuk led the KHL in scoring last season, registering 31 goals and 32 assists for 63 points in 53 games.
Kovalchuk also recorded seven points in six games for the Olympic Athletes from Russia team that won gold at the 2018 Winter Games in Pyeongchang, South Korea.
During his NHL tenure, Kovalchuk was among the best pure scorers in the league.
In 816 NHL regular-season games, Kovalchuk racked up 417 goals and 399 assists for 816 points.
He also had 27 points in 32 playoff games, including 19 during New Jersey's run to the Stanley Cup Final in 2011-12.
Kovalchuk was originally selected by the Thrashers with the No. 1 overall pick in the 2001 NHL draft.
He played in three NHL All-Star Games, scored 40 or more goals in a season on six occasions and netted 30 or more goals nine times.
In 2003-04, he won the Maurice "Rocket" Richard Trophy as the league's leading goal scorer.
Kovalchuk will join a Kings team that was swept in the first round of the playoffs last season by the expansion Vegas Golden Knights.
While L.A. led the NHL in goals allowed, it was just 17th in scoring.
He will provide the Kings with some much-needed offensive punch and could be the ideal sidekick to center Anze Kopitar, who was a finalist for the Hart Trophy.
With Jeff Carter, Dustin Brown, Tyler Toffoli, Tanner Pearson and Adrian Kempe also in the mix, the Kings should be a far more dangerous team on the attack in 2018-19.