The deal reportedly comes with an average annual value of $6.25 million, according to TSN's Darren Dreger.
Kovalchuk is 35 years old and five years removed from the NHL, but has remained productive overseas, collecting 31 goals and 63 points in 53 games this past season with SKA St. Petersburg of the KHL.
"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," said Kings general manager Rob Blake.
Kovalchuk was eligible to negotiate with teams and agree to terms on a deal since being activated off the voluntary retirement list April 15, but he cannot officially sign a contract until free agency opens July 1.
Multiple teams had interest in acquiring Kovalchuk's services, but the Russian sniper was ultimately most interested in L.A.'s three-year offer.
The Kings finished 2017-18 with the league's 17th-ranked offense, and only had three players with at least 20 goals.
As a left winger, Kovalchuk immediately slides to the top of the team's depth chart at that position, and will likely play alongside either Anze Kopitar or Jeff Carter on one of the Kings' top two lines.