Carter, 27, is expected to supply some offense for the goal-starved Kings, who started Thursday night in eighth place in the Western Conference.
"Jeff is a proven goal scorer in our league," Kings general manager Dean Lombardi said. "He brings goal-scoring abilities, speed, and at his age he is entering the prime of his career. We also like his versatility as he can play both center and wing."
Carter signed an 11-year, $58 million deal with the Philadelphia Flyers in November 2010 but now will be joining his third team since agreeing to it.
Acquired in a blockbuster deal with Philadelphia last summer, Carter was expected to center the Blue Jackets' top line with captain Rick Nash, who is also rumored to be on the trading block leading up to Monday's NHL dealing deadline. But Carter missed 20 games with a broken foot and a separated shoulder. He had three goals in the Blue Jackets' previous game and has 15 goals and 10 assists in 39 games this season.
Carter will now be reunited with forward Mike Richards, who was traded by the Flyers to the Kings last June on the same day Carter was shipped to Columbus in a major Philadelphia housecleaning.
"I am obviously excited," Carter told the Kings' website. "I am familiar with the team and a lot of guys on the team. ... I looked at the Kings at the start of the year as being a club in a good position to win. I look forward to coming to L.A."
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.
"I am excited by this," Johnson told the Columbus Dispatch, "to go to a team that wants me and to play in a great sports city."
If the Kings make the playoffs this season, they will send their first-round pick this summer to the Blue Jackets. If Los Angeles fails to qualify, Columbus will have the choice of taking this year's pick or next year's top selection.
"Jack is a talented young defenseman who will strengthen our defense corps. We are very excited to add him to our organization," Columbus general manager Scott Howson said in a statement. "We are committed to reshaping our club and moving forward. Adding a player like Jack and a first round pick are important parts of that process."
Carter has scored at least 30 goals three times, and has hit the 20-goal mark five times during his six-plus seasons in the NHL.
In 343 NHL games, Johnson has 30 goals, 94 assists and 256 penalty minutes.
Johnson, who is expected to switch from jersey No. 3 to No. 7 in Columbus, became expendable with the rapid development of 22-year-old defenseman Slava Voynov, Lombardi said during a conference call Thursday.
"The only way we can make this deal is because we have so many young D-men in the system," he said.
Carter is expected to arrive in Los Angeles on Saturday night, meaning he will not be available for that evening's game against the visiting Blackhawks.
Lombardi insisted he wasn't pushed to make the deal because of Monday's impending trade deadline.
"This isn't your classic trade deadline deal," Lombardi said. "This is a good young player for a good young player. This is a hockey deal."
Columbus has sought to remold its team after a disappointing season. The Blue Jackets (18-35-7) are last in the NHL, by far, in wins and points.
Information from Dan Arritt, who covers the NHL for ESPNLosAngeles.com, and The Associated Press was used in this report.