The Blue Jackets will reportedly receive forward Matt Frattin and two conditional picks in return, but will have to pay a portion of Gaborik's remaining salary for this season.
It's the second straight season in which Gaborik has been dealt late in the campaign. He played just 34 games in Columbus since moving from the New York Rangers in 2013.
Gaborik ranks 15th among active players with 342 goals in 791 games in a career that began with nearly eight seasons with the Minnesota Wild. He has added 346 assists for 688 points, with 91 power-play markers.
Injuries have long been an issue for Gaborik, as he's missed last 15 games in a season on six occasions.
The 32-year-old Slovakian forward is set to be an unrestricted free agent on July 1.
The Kings, despite being a Stanley Cup contender, rank just 27th in goals.
Frattin had just two goals and six assists in 46 regular-season and playoff games with Los Angeles. He was acquired by the club in the deal last summer that saw Jonathan Bernier head to Toronto.
For his career, he has 17 goals and 17 assists in 122 regular-season games in the NHL after playing collegiately at the University of North Dakota.