Carter is expected to supply some offense for the goal-starved Kings, who started Thursday night holding the eighth and final playoff spot in the Western Conference.
Acquired in a blockbuster deal with Philadelphia last summer, Carter was expected to center the top line for Columbus with captain Rick Nash. But Carter missed 20 games due to a broken foot and a separated shoulder. He had three goals in the Blue Jackets' last game and has 15 goals and 10 assists in 39 games.
Carter now joins former Flyers Mike Richards and Simon Gagne in Los Angeles.
Johnson, a 25-year-old former University of Michigan star, has eight goals and 16 assists this season - his fifth in the NHL, all with the Kings.