The 32-year-old Vermette was dealt by the Coyotes to the Chicago Blackhawks on Feb. 28 due to his impending free agency.
The right winger saw his role on the talented Blackhawks recede, resulting in just 14:04 minutes of ice time per game, as opposed to the 18:59 he averaged with Arizona. He did not score in 19 appearances with the Blackhawks and collected three assists.
Vermette, though, played a part in Chicago's run to its third Stanley Cup in six seasons with four goals and three assists in 20 games.
His goal tally included two game-winning goals in the Stanley Cup finals. He notched a plus-5 rating in the playoffs in an average of 13:08 per game. He also scored the game winner in double-overtime to tie the Anaheim Ducks at 2-2 in the Western Conference finals.
Information from ESPN.com's Pierre LeBrun and Craig Custance was used in this report.