Columbus received right wing Matt Frattin, a second-round draft pick and a conditional third-round pick in exchange for Gaborik, the Blue Jackets announced.
Gaborik, 32, has appeared in just 22 games this season due to a collarbone injury, and has six goals and 14 points.
"Gaborik wanted it to work and we wanted it to work," Blue Jackets general manager Jarmo Kekalainen said. "But it didn't, and we both had to move on."
It marks the second straight season that Gaborik has been dealt prior to the trade deadline. The Blue Jackets acquired Gaborik last season from the New York Rangers.
"You can have a big name and a big career, but it can be hard to find a fit somewhere," Kekalainen said. "He just didn't fit."
Gaborik has 342 goals and 688 points in parts of 13 seasons with the Blue Jackets, Rangers and Minnesota Wild.
The Kings also acquired defenseman Brayden McNabb from the Buffalo Sabres along with forward Jonathan Parker and two second-round draft picks in exchange for forwards Hudson Fasching and Nicolas Deslauriers. The Kings then sent forward Linden Vey to the minors to clear salary-cap space on the big league roster for Gaborik.
McNabb is expected to join the Kings' AHL affiliate in Manchester, but general manager Dean Lombardi sees a major role for the tough-nosed defenseman in Los Angeles in the near future.
McNabb played in 37 games for Buffalo since late 2011, recording one goal and seven assists. He played 12 games for the Sabres this season and 38 for their AHL affiliate in Rochester.
"Given where our team was at, it was going to be at some point critical to get a young defenseman who has a chance to play in your top four," Lombardi said. "He's closer to being ready than if I had to go after a kid who was still in junior."
Fasching was a fourth-round pick by the Kings last summer, and Deslauriers was a third-round pick in 2009 who moved from defenseman to left wing this season in Manchester for his first professional season.
Los Angeles also signed promising goalie Patrik Bartosak to a three-year entry-level contract, and the Kings acquired minor league forward James Livingston from San Jose at the deadline for a seventh-round pick in 2016.
ESPN.com's Pierre LeBrun and The Associated Press contributed to this report.