Financial terms were not disclosed, but sources told TSN of Canada that the deal is worth $2.5 million.
Carter, who has played nine years in the NHL, is coming off a career-best 33-goal season with Vancouver.
The Blue Jackets hope he will serve as the big, physical player they have been missing on their top lines. He could also spark the offense for Columbus, which still hasn't signed young Russian star Nikolai Zherdev. The forward's agent and the Blue Jackets' front office have traded threats and contentious talk throughout the summer.
Carter also had 22 assists for 55 points in 81 games last season. He led the Canucks in goals, power-play goals (15), game-winning goals (seven) and shooting percentage (22.6 percent).
He has played in 610 career NHL games with 191 goals and 202 assists. Since 1998, the right winger has averaged 23 goals a season and has scored 10 or more power-play goals in three of four campaigns.
"Anson Carter is a big, strong power forward who is a proven 25- to 30-goal scorer," Columbus general manager Doug MacLean said.
The 6-foot-1, 210-pound Carter has also played for Washington, Boston, Edmonton and the New York Rangers. The Toronto native helped Canada win gold medals at the 1997 and 2003 world championships and the 1994 world junior championships.
Information from The Associated Press was used in this report.