The deal is pending both players passing a physical, while Columbus will also get a conditional first round draft pick in either 2012 or 2013.
In Los Angeles, Carter is reunited with former Philadelphia teammate Mike Richards. The two played six seasons together with the Flyers before being dealt in separate trades over the summer.
Carter, 27, has struggled this season as he has posted just 15 goals and 10 assists over 39 games with the Blue Jackets.
The 11th overall pick of the 2003 draft, Carter has totaled 196 goals and 172 assists.
"Jeff is a proven goal scorer in our league. He brings goal-scoring abilities, speed and at his age he is entering the prime of his career," said Los Angeles general manager Jack Lombardi. "We also like his versatility as he can play both center and wing."
Johnson, who was chosen third in the 2005 draft by Carolina, has played his entire career in Los Angeles and over 343 games he has notched 30 goals and 94 assists.