Pettersson, 30, is entering his 10th year after coming off the worst season of his career, after putting up a career-low 18 points (3 goals, 15 assists) in all 82 games.
The veteran will now be joining his third team in three years as the Rangers continue to make moves this offseason; others include the acquisitions of Pavel Dorofeyev from the Golden Knights and Massimo Rizzo from the Nashville Predators.