The 27-year-old center has scored 15 points (seven goals, eight assists) in 49 games for the Canucks this season.
Selected by the Chicago Blackhawks in the fourth round (No. 121) of the 2013 NHL Draft, Motte has scored 62 points (35 goals, 27 assists) in 260 NHL games through seven seasons with the Blackhawks, Columbus Blue Jackets and Canucks and five points (four goals, one assist) in 17 Stanley Cup Playoff games.
"Just a good all-around pro who can do a lot of good things, PK and in the bottom six of your lineup," Rangers general manager Chris Drury said of Motte. "He plays extremely hard and competitive. He's a high-character guy I think will fit in nicely."
RELATED: [2021-22 NHL Trade Tracker]
The Rangers (40-18-5) are tied with the Pittsburgh Penguins for second place in the Metropolitan Division, three points behind the first-place Carolina Hurricanes.
Also Monday, New York acquired forward Andrew Copp from the Winnipeg Jets for three NHL Draft picks and forward Morgan Barron; defenseman Justin Braun from the Philadelphia Flyers for a third-round pick in the 2023 draft; and forward Nick Merkley from the San Jose Sharks for defenseman Anthony Bitetto.
Forward Frank Vatrano was acquired by the Rangers from the Florida Panthers on March 16 for a fourth-round pick in the 2022 NHL Draft, the lower pick of New York's selection or Winnipeg's selection previously acquired by the Rangers.
NHL.com senior writer Dan Rosen contributed to this report