The Marlins also included cash in the deal to help offset the $9 million that was left on the three-year, $27 million contract that Bell signed with Miami in December 2011.
The Rays and Hanigan agreed to a three-year contract extension covering the 2014, '15 and '16 seasons, with a club option for '17, worth a guaranteed $10.75 million. He will make a donation to the Rays Baseball Foundation.
"Ryan Hanigan is a tremendously talented defensive catcher," said Rays executive vice president of baseball operations Andrew Friedman. "[He] really shuts down the run game, [and] takes a lot of pride in what he does behind the plate. And we also like what he can do in the batter's box, especially against left-handed pitching. He's a guy we've had our eye on for a while, and so when we had the opportunity to acquire him, we were aggressive to do so."
Tampa Bay will go to camp with three catchers: Hanigan, Jose Molina and Jose Lobaton. Hanigan didn't sound worried about where he fit in with his new team.
"That's to be determined as far as playing time and all of that stuff," Hanigan said. "I'm just excited about the situation. They've created such a competitive team down here, obviously in the AL East. Everyone I've talked to has great things to say about [manager] Joe [Maddon] and the organization. ... I'm just looking forward to helping the team compete."
Hanigan, 33, became expendable when the Reds signed free-agent catcher Brayan Pena to a two-year, $2.275 million contract last month.
"It was tough to trade Hanigan," Cincinnati general manager Walt Jocketty said. "It got to the point where we had one year before he became a free agent. Sometimes you have to make some tough business decisions you don't like to make. Hani did a terrific job for this organization. Everybody really likes him as a person, as well as a player. We also tried to keep in mind places where he might want to play. I know Tampa was an area. They had interest in him for a couple of years. Hopefully this works out well for him."
Hanigan said he wasn't sure what the Reds planned to do with him.
"Then when they signed Brayan, I kind of felt like they were going in a different direction," Hanigan said. "But I understood what they were doing, and after that happened, I kind of just took it in stride and developed a relationship with [the Rays] when I was allowed and got to know these guys on a fairly quick basis."
Respected for his defensive and game-calling skills and his ability to get on base as a patient hitter, Hanigan still endured the worst offensive season of his career in 2013.
Limited to 75 games, Hanigan batted .198 with a .306 on-base percentage, including two homers and 21 RBIs. Injuries nagged the catcher throughout a season that included two stints on the disabled list because of a strained left oblique and a sprained left wrist.
Friedman allowed that Hanigan's health and his willingness to extend his deal were both factors.
Behind the plate, Hanigan worked with a rotation that had four starters throw 200 innings in 2012 and had a Major League-best 3.04 catcher's ERA. His caught-stealing percentages -- 48 percent in '12 and 45 percent in '13 -- were both best in the National League.
This season, Hanigan caught three of Cincinnati's five complete games and 10 of the staff's 17 shutouts, including Homer Bailey's no-hitter in July. Now he could work with David Price, Matt Moore, Jeremy Hellickson, Alex Cobb and Chris Archer.
"Those are some guys right there, for sure," Hanigan said. "It's going to be a fun deal. I'm just going to take it in stride and see what these guys got. And I've got some work to do now, I've got some video to see."
Bell, 36, has recorded 168 career saves over 10 Major League seasons with the Mets, Padres, Marlins and D-backs.
"Heath Bell is also a guy that we've liked for quite a while," Friedman said. "He's still got really good stuff. He missed a lot of bats this year, commanded the zone better than in years past, just a lot of good indicators that we feel can put him in a position to come here and have a lot of success."
Bell's 166 saves over the past five seasons rank third in the Major Leagues after Jonathan Papelbon (173) and Mariano Rivera (170).
"I feel like it's a fresh start," Bell said. "They already asked me what number I want. I told them that, 'Hey, I want you guys to pick it. I want to show up and get people out. This is a fresh start for me, so I want to leave it to you guys what number you give me, and I'll be surprised at Spring Training when I get there.' ... Anything I can do to help out, I'm glad to do."
With the departure of Fernando Rodney, who has closed for the Rays the past two seasons, it's easy to assume Bell will be the closer. However, Friedman would not anoint Bell in that role, which seemed fine with Bell.
"I kind of feel like I have a shot at winning the ninth-inning job," Bell said. "But I see my job as coming into Spring Training and showing them what I can do. ... They've always said I don't back down from anybody. I go right after everybody. So I feel like I want to help the team out the best way I can. I feel like it all depends on what I do in Spring Training for what kind of role I have."
In 2013, Bell went 5-2 with 15 saves and a 4.11 ERA in 69 games for Arizona. He recorded 72 strikeouts and only 16 walks, establishing a career-best 2.19 walks per nine innings.
Choate, 22, pitched to a 2.88 ERA with 7.7 K/9 and 2.0 BB/9 ratios in 16 relief appearances for Hudson Valley of the New York-Penn League in 2013. The Texas native was signed by Tampa Bay as an undrafted free agent in June.
Tuesday's trade marked the third three-team trade in Rays history, the first in a decade and the first under Friedman. The last such deal occurred on Dec. 14, 2003, when Tampa Bay dealt left-hander Joe Kennedy to the Rockies and acquired left-hander Mark Hendrickson from the Blue Jays. The other occurred on Jan. 8, 2001, when the Rays sent right-hander Roberto Hernandez to the Royals and right-hander Cory Lidle to the Athletics and received outfielder Ben Grieve from Oakland.