"Antoine is the consummate professional and a class act and we wish him the best of luck in the future," Coyotes general manager Don Maloney said in a statement.
Vermette, 32, has 13 goals and 22 assists in 63 games this season. He was leading Coyotes forwards with an average ice time of 18:54. He also led the team's forwards in power-play and penalty-kill ice time. He's eighth in the NHL, one spot behind the Blackhawks' Jonathan Toews, with a 56.0 faceoff winning percentage.
Vermette has 194 goals and 236 assists in 815 career regular-season games and has nine goals and nine assists in 58 career playoff games. He reached the Stanley Cup finals with the Ottawa Senators in 2007.
Vermette has a cap hit of $3.75 million and is in the final season of his contract. He will become an unrestricted free agent after the season.
After Arizona's 4-1 loss in Boston, a visibly emotional Vermette discussed the possibility of having played his last game for the Coyotes.
"I don't know what I'm thinking. It's obviously a strange position and it's not a fun one," Vermette said before the trade. "I am [emotional] but you've got to take it, man. It's part of the game."
Dahlbeck, 23, has four goals and six assists and is a plus-2 in 49 games with the AHL's Rockford IceHogs this season. He was a healthy scratch for the IceHogs on Saturday. Chicago drafted Dahlbeck in the third round in 2011 and he made his NHL debut Dec. 6, 2014, at Nashville. The Swede netted one goal in four games with the Blackhawks.
"Klas Dahlback is a big, strong, two-way defenseman who skates well and competes hard," Maloney said.
Blackhawks general manager Stan Bowman said he would likely seek a defenseman and forward before Monday's trade deadline after Patrick Kane fractured his clavicle on Tuesday. Kane is expected to be out 12 weeks.
The Associated Press and ESPNBoston.com's Joe McDonald contributed to this report.