The trade was announced Friday by the Angels.
The Braves once regarded Hanson, 26, as a staff ace-in-waiting, but he has been bothered by shoulder problems and a worrisome decline in velocity as his career has progressed. According to FanGraphs, the average radar gun reading for Hanson's fastball declined from 92.7 mph in 2010 to 91.2 in 2011 to 89.7 this past season.
Hanson was 10-5 with a 3.71 ERA before the All-Star break last season and 3-5 with a 5.69 ERA in the second half. He was on the disabled list from July 31 to Aug. 17 with a lower back strain.
"I think toward the end, I didn't feel I was as strong as I need to be," Hanson said of last season. "I think as the years have gone along I've learned how to have a better understanding of how to stay healthy and be strong. I think it was a little bit of a learning experience last year and I'm looking to improve."
Despite suffering a mild concussion in a one-car accident during spring training, Hanson won a career-high 13 games. His ERA, though, increased in each of his four seasons with the Braves -- from 2.89 to 3.33 to 3.60 to 4.48.
"I don't know that we're necessarily looking for a bounce back," Angels general manager Jerry Dipoto said. "He won 13 games. I don't think it would be fair to qualify it as a disappointing season. ... His velocity remained consistent from month to month. Our scouting reports remained consistent with what we've always thought of Tommy. He's done it for four years at the big league level, and we think he'll continue to do it."
Hanson also is expected to earn about $4 million next season as a first-year arbitration-eligible player, so the Braves had been looking to trade him as a way to help cut costs.
Still, the right-hander brings needed depth to the Angels' rotation behind Jered Weaver and C.J. Wilson. The Angels traded Ervin Santana to the Royals earlier this offseason and declined to pick up the contract option on Dan Haren.
Walden was the Angels' primary closer in 2011 but battled a shoulder injury in 2012 and pitched primarily in middle relief. He became expendable after the Angels signed free agent Ryan Madson to a one-year contract this week.
If Walden is healthy, he brings a power arm to an Atlanta bullpen headed by Craig Kimbrel, Jonny Venters and Eric O'Flaherty. He struck out 67 batters in 60 1/3 innings in 2010, saved 32 games and made the American League All-Star team as a rookie.
But Walden, like Hanson, has been sidetracked by injuries and unorthodox pitching mechanics.
"We've been focused on adding a power arm to our bullpen all offseason," Braves general manager Frank Wren said. "We felt if we added one power arm we would have a bullpen that would stack up with the best bullpens in our league. Jordan Walden has closing experience and the kind of arm that will stack up well in a seventh- and eighth-inning role for us."
Information from The Associated Press was used in this report.