Arizona acquired Cabrera earlier on Saturday from the A's as part of a major deal. Outfielder Chris Young was sent to Oakland for shortstop Cliff Pennington and Cabrera, a 22-year-old who played high school ball in Lakeland, Fla.
Cabrera was immediately sent to Miami for Bell, who had a rocky '12 with the Marlins.
"This should be a positive change for Heath and the Marlins," Marlins president of baseball operations Larry Beinfest said in a statement. "After a disappointing 2012 season, Heath gets a fresh start and this move gives us clarity as we begin our offseason roster improvement."
The trade frees up some money for the Marlins, who signed Bell to a three-year, $27 million contract on Dec. 7, 2011.
The D-backs, according to a source, will pick up $13 million of the remaining $21 million owed to Bell through 2014.
Bell had a $6 million base salary in 2012. The contract included a $3 million signing bonus, which was deferred without interest.
In 2013 and '14, Bell will make $9 million in each season.
The Marlins are coming off a tumultuous season, when they finished last in the National League East with a 69-93 record.
Bell had his struggles, converting 19 of 27 save chances, and he lost his closer role to Steve Cishek after the All-Star Break.
In 73 games, Bell was 4-5 with a 5.09 ERA.
A three-time All-Star with the Padres from 2009-11, the outspoken veteran also was the center of some controversy in late September for comments he made regarding manager Ozzie Guillen on "The Dan Sileo Show" on 560 WQAM in Miami.
"It's hard to respect a guy that doesn't tell you the truth or doesn't tell you face-to-face," Bell said during the radio interview that aired on Sept. 24.
The day after his remarks gained national attention, Bell said: "I did not mean anything towards Ozzie in that aspect. But [media reports] wrote it that way. So everybody interpreted it that way. So now apparently I'm backtracking everything I said."
On the last day of the season, Guillen was asked about what went wrong for Bell.
After all, from 2009-11, the right-hander's 132 saves were the most of any closer in the Majors. Yet, in the first half alone, Bell converted 19 of 25.
"I think he just had a bad year," Guillen said on Oct. 3, the last day of the season. "His velocity was there, but he didn't throw strikes. That's the way I look at it; maybe he saw something different. He did not command his breaking ball and he got in trouble."
Bell lost his closer role after the last game before the All-Star Break. In a game at St. Louis, he was called upon to lock down a two-run lead in the ninth, but he gave up three runs in a heartbreaking loss.
In the second half, Cishek took over at closer, and he now will hold the title entering Spring Training.
Bell had one ninth-inning save opportunity in the second half. On Sept. 8 at Washington, the veteran tried to preserve a one-run lead in the ninth inning, but Jayson Werth led off the inning with a game-tying home run. Miami eventually lost in extra innings.
On Oct. 2, his last appearance as a Marlin, Bell suffered a blown save when he gave up a run in the eighth inning against the Mets.
Overall, Bell enjoyed a solid second half in a setup situation, posting a 3.10 ERA after the All-Star Break. In the first half, his ERA was a startling 6.75.
By trading Bell, the Marlins avoided some more controversy regarding who would close in 2013.
The 26-year-old Cishek will get the nod without the presence of Bell in camp remaining a fallback option.
Cishek was the Marlins' best reliever. With his deceptive side-arm delivery, he finished 5-2 with a 2.69 ERA, and he had 15 saves in 19 opportunities.
In Cabrera, the Marlins add a young player who may factor into their third base situation in the future. Ranked No. 16 on the A's Top 20 Prospects list at the time of the trade, he slides into the No. 20 spot on the Marlins' list.
The Santo Domingo native was Oakland's second-round pick in the 2010 First-Year Player Draft out of Lakeland High School. He spent all of '12 at Class A Stockton in the California League, where he batted .232 with nine doubles, two triples, three home runs and 21 RBIs. He was limited to 60 games due to a right hip strain.
Cabrera is currently playing in the Arizona Fall League for the Phoenix Desert Dogs.