The power-hitting second baseman, coming off the best offensive season of his career, was exchanged for left-handed pitcher Mike Dunn and infielder Omar Infante.
"Dan gives us the right-handed power we have been looking to add to the middle of our lineup for the last couple of years," Braves general manager Frank Wren said in a statement. "There are not many of those guys out there."
Uggla hit .287 with 33 home runs and 105 RBIs for the Marlins last season, ranking fifth in the National League for homers and RBIs.
The 30-year-old leads all second basemen in the majors in home runs since he broke in with the Marlins in 2006. He ranks 13th on the all-time home run list for second basemen.
(Editing by Mark Lamport-Stokes in Los Angeles)