Rangers general manager Chris Drury announced the move on Tuesday.
Gauthier had three goals and four assists in 49 games this past season, with the goals and assists being career highs. The 24-year-old has five goals and 13 assists in 96 career NHL games, split between the Rangers and Carolina Hurricanes.
Gauthier played his first five games with the Hurricanes in 2019-20 before being traded to New York on Feb. 18, 2020. He was selected by the Hurricanes with the 21st pick of the 2016 draft.