In exchange, the Blue Jackets receive a 2012 second-round draft pick (acquired by the Coyotes from the Ottawa Senators in the Kyle Turris trade); a conditional fifth-round pick in 2013; plus minor league goalie Curtis McElhinney.
"We are extremely pleased to acquire Antoine," Coyotes general manager Don Maloney said. "He is a smart, skilled, two-way center who will be a great addition to our lineup."
The fifth-round pick in 2013 becomes a fourth-round pick if the Coyotes win a playoff round this year, a source said.
The trade needed the NHL's blessing, another source said, because the Coyotes still are owned by the league as it continues to find a new owner.
Vermette has three more years left on his deal after this season, with an annual $3.75 million salary and cap hit.
The Blue Jackets, with the worst record in the NHL, have been trolling for trade partners for the past few weeks. Captain Rick Nash and high-priced center Jeff Carter both have been bandied about as trade targets. Instead, for now, the Blue Jackets dealt Vermette, who has eight goals and 19 assists in 60 games this season.
McElhinney's acquisition could open the door to the team trading goalie Curtis Sanford, who will be an unrestricted free agent this summer. He is recovering from a back injury.
The Blue Jackets also have former Calder Trophy goalie Steve Mason, who has been erratic since being named the league's top rookie in 2009.
Pierre LeBrun covers the NHL for ESPN.com. Information from The Associated Press was used in this report.