Vanek is an unrestricted free agent after this season.
Since the start of the 2013-14 season, Vanek has played for seven teams: the Sabres, Canadiens, Islanders, Wild, Panthers, Red Wings and Canucks.
This is the fourth time he has been traded in the past five seasons. The 33-year-old is currently playing on a one-year, $2 million contract he signed with the Canucks as a free agent during the offseason.
Despite the constant movement, Vanek has continued to produce, as he is on pace for more than 20 goals and 50 points this season.
"Thomas Vanek is probably one of the best power-play players in the league and a consistent goal scorer and can add some offense to our team," Columbus general manager Jarmo Kekalainen said.
The Blue Jackets, who hold the second wild card in the East, also added defenseman Ian Cole ahead of the deadline.
Cole, who won two Stanley Cups with Pittsburgh, was in the Blue Jackets locker room before the game.
"I'm very excited," Cole said. "They have a great team here, and I'm happy to be a part of it."
He said his role will be to "play some solid defense, play hard and get pucks to these skilled forwards as quickly as we can."
The Associated Press contributed to this report.