In return, the Coyotes got defenseman Dmitri Kalinin and forwards Petr Prucha and Nigel Dawes. Morris has five goals and seven assists in 57 games this season, but had been held out of the lineup in the days leading up to the deadline to avoid injury that could have prevented a trade.
In 775 career NHL regular-season games, Morris has 76 goals and 256 assists.
Washington, Boston and Philadelphia had all been involved in discussions with the Coyotes about Morris, but when a deal couldn't be struck with one of those teams, the Rangers became an option early Wednesday.
Morris, 30, was the 13th overall pick in 1996 and will be an unrestricted free agent in July.
"Morris is a good, solid defenseman. He gives us a little more bite in the back end. He can play a little bit of everything -- a little offense, a little defense. He's an aggressive defenseman," Rangers general manager Glen Sather said during a conference call.
Coyotes general manager Don Maloney served as the Rangers' assistant GM under Sather for several years before moving on to Phoenix.
"Donnie knew these guys well and he's liked the way they've performed," Sather said of the players sent to the Coyotes. "He's certainly changed the chemistry of his team. These guys are both good, solid people and he was looking for somebody like that. I don't think it was that complicated for him to make the deal."
Antropov, 29, has spent all nine of his years with the Leafs, and is in the final year of a two-year deal. He is eligible to become an unrestricted free agent on July 1.
Antropov, who is 6-foot-6, 230 pounds, has 21 goals and 25 assists this season.
"Antropov is a big winger or center iceman," Sather said during the conference call. "He's a gifted goal scorer and I think he'll help us in the goal-scoring department. He's a talented guy."
Information from ESPN.com's Scott Burnside and The Associated Press contributed to this report.