The Rangers are receiving a conditional second-round draft pick this year and a conditional third-round pick in the 2020 draft in the deal announced Saturday night.
Zuccarello had 113 goals and 239 assists in 509 games over parts of nine seasons in New York. This season, he had 11 goals and 26 assists in 46 games.
“He’s gonna bring some more scoring, he’s an offensive player, so he’s going to bring some offensive capabilities to us,” Stars general manager Jim Nill said. “He’s an energetic player, real puck chaser and just plays the game the right way.”
The 31-year-old Norwegian goes from a Rangers team in rebuilding mode to a Stars team that is tied with Colorado for the wild card spots in the Western Conference.
Earlier in the day, Dallas acquired defenseman Ben Lovejoy in a trade with New Jersey.