The average annual value of the contract is $6.25 million, a source told ESPN.
"We are excited to add Ilya to the LA Kings organization," vice president and general manager Rob Blake said in a statement. "He gives us an added element of skill and scoring along with a desire to win. We will withhold further comment until July 1."
Kovalchuk, 35, hasn't played in the NHL since 2013, when he returned to Russia to play for SKA St. Petersburg of the Kontinental Hockey League.
He was the subject of a free-agency sweepstakes when he announced his intention to return to the NHL. He led the KHL with 63 points last season, and he was second with 31 goals scored.
Kovalchuk was the No. 1 pick of the 2001 draft by the Atlanta Thrashers. He was the first Russian player to be selected first in the NHL draft. Over his 11 NHL seasons, no active player scored more goals than Kovalchuk's 417.
He scored 816 points (417 goals, 399 assists) in 816 regular-season games with the Thrashers and New Jersey Devils.
Kovalchuk's first contract with the Devils was famously spiked by the NHL for cap circumvention. The Devils then signed Kovalchuk to a 15-year, $100 million contract in 2010. Kovalchuk "retired" just three years into that deal, saying he had soured on the NHL after the 2012 lockout for reasons that included escrow withholding and North American taxes.
He also said he wanted to be closer to family, walking away from $77 million owed by the Devils to sign a four-year deal with SKA St. Petersburg.
The Kings were a suitor for Kovalchuk in 2010 before he chose the Devils.
Los Angeles rebounded from a poor 2016-17 campaign to make the playoffs this past season, but the Kings were swept in the first round of the Stanley Cup playoffs by the Vegas Golden Knights.
Several teams made pitches to Kovalchuk's agent JP Barry this past week, including the Boston Bruins.
"We put our position forth," Bruins GM Don Sweeney said Friday. "He's got plenty of options that he's mulling over as we discussed, and he said he'd get back to us."
Kovalchuk, a three-time NHL All-Star selection, won two KHL titles with St. Petersburg. He also was the MVP in Pyeongchang as the Russians won the Olympic gold medal.
He has stated that his goal is to win a Stanley Cup, so he can match Russian teammate Pavel Datsyuk, who has won an Olympic gold medal, a world championship and a Stanley Cup title.