In return, the Hurricanes receive a second-round pick in 2016 and 2017, plus Finnish prospect Aleksi Saarela.
Staal had to waive his no-move clause to accept the deal. The Hurricanes' captain has spent his entire 12-year career with the club and is eligible to become an unrestricted free agent this summer, once the final year of his seven-year, $55.75 million contract expires.
"As much as I think they're doing the right thing with the young players -- there's some great pieces there for the future -- I think deep, deep in my gut this was an opportunity I needed to take,'' Staal said Monday, hours before his debut with the Rangers against the Columbus Blue Jackets.
Rangers general manager Jeff Gorton said the Hurricanes retained a portion of Staal's $8.25 million cap hit, and the Rangers have enough financial flexibility to add another "small-salary player if we wanted to."
The Rangers trail first-place Washington by 16 points in the Metropolitan Division standings.
"We felt like he was one of the best, if not the best, player available on the market to give us what we're looking for in our top nine," Gorton said. "And that's why we made the move."
The deal -- finalized about an hour before the Hurricanes played host to the St. Louis Blues and a day before the NHL trade deadline -- wasn't a total surprise from Carolina's perspective.
After a rocky start, Carolina mounted a late push for its first playoff berth since 2009, but lost four of six entering Sunday's game. The Hurricanes were four points behind the Pittsburgh Penguins for the final wild-card spot, and the Penguins had three games in hand.
"When you miss the playoffs for six years and you're the leader, the captain, it's tough,'' Staal said. "There was a lot of trying times. For a lot of different reasons, it didn't happen the way you envisioned. For me it was time for this opportunity and this chance.''
The trade leaves goalie Cam Ward -- who earned the Conn Smythe Trophy in 2006 as the franchise won its only Stanley Cup -- as the only Hurricane left from any of the club's playoff teams.
"Eric has been the face of this franchise for a long time, and we thank him for his dedication, leadership and many contributions," Hurricanes general manager Ron Francis said. "We felt this was an important opportunity for us to continue our work in building an organization that can consistently compete in the Stanley Cup playoffs."
The 31-year-old Staal leaves one younger brother, Jordan Staal, and will be united with another brother, Marc Staal, who plays defense for the Rangers. A fourth Staal brother, Jared, is playing with South Carolina of the ECHL and had been in the Hurricanes' organization.
The Rangers tweeted pictures of the two Staal jerseys on Monday:
"I think it'll help. He probably knows a lot of players on our team because of Marc," Gorton said. "But at the end of the day, it wasn't really that I or anybody here felt like if we bring him here he's going to be more comfortable because of what Marc's doing. It's all about Eric."
The eldest Staal is a four-time All-Star and has scored 30-plus goals five times in his career, and has 10 goals and 23 assists in 63 games this season.
"We're looking at a player that we think can be energized by this trade," Gorton said.
Staal is the Hurricanes' career leader in nearly every category, including 909 games played, 332 goals and 775 points. The only other players in the history of the Hartford-Carolina franchise who have skated in more games are Francis and Glen Wesley, whose numbers are hanging from the PNC Arena rafters.
"Eric, for me being here six years, is the only captain I've had," forward Jeff Skinner said. "He's been here for my whole career. He's a great person and you won't meet a better guy in the league."
Saarela was the Rangers' third-round pick in last year's draft. He currently plays for Assat Pori of the Finnish elite league. The 19-year-old leads the team with 18 goals, and his total of 31 points in 46 games is good for second on the team.
Information from The Associated Press was used in this report.