The 30-year-old Jokinen had 21 goals and 21 assists in 57 games in his first season with Phoenix. He has 229 goals in 780 career NHL games with Los Angeles, the New York Islanders, Florida and Phoenix.
The Coyotes acquired center Matthew Lombardi, right wing Brandon Prust and a conditional first-round pick. Phoenix sent a third-round 2009 draft pick to Calgary as part of the transaction.
Phoenix then sent free-agent-to-be Derek Morris to the New York Rangers for fellow 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.
Coyotes general manager Don Maloney served as the assistant GM of the Rangers under Glen 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."
The Morris deal was the second completed by the Rangers before Wednesday's NHL trade deadline as they acquired veteran center Nik Antropov from the Toronto Maple Leafs for a second-round draft pick and a conditional draft pick.
The 6-foot-6, 230-pound Antropov has 21 goals and 25 assists in 63 games this season.