Smyly, 31, was 0-1 with a 3.42 ERA in five starts and two relief appearances last season for San Francisco, which signed him to a one-year major league contract in January.
Smyly was 4-7 with a 6.24 ERA in 21 starts and four relief appearances in 2019 for Texas, which released him in June of that year, and Philadelphia, which signed him one month later.
He is 35-35 with a 4.13 ERA for Detroit (2012 to 2014), Tampa Bay (2014 to 2016), the Rangers, Phillies and Giants. He had Tommy John surgery in 2017 and spent most of the 2018 season recovering.
"This is an upside play, no doubt about it,'' general manager Alex Anthopoulos said. "Obviously, we'll find out eight months from now, 10 months from now how it worked out. But we think Drew has tremendous upside. He's only scratched the surface.''
The lefty has abandoned his changeup, Anthopoulos said, focusing on his curveball and cutter.
"We feel like he's just about to really emerge to have the best years of his career,'' the GM said "Once we made that determination, we signed him to a healthy, strong deal. Hopefully all sides will win and he'll have a great year.''
Smyly adds depth and experience to an Atlanta rotation led by Max Fried, who finished fifth in the NL Cy Young Award voting, and rookie sensation Ian Anderson. The Braves also are counting on the return of Mike Soroka, who missed most of this past season with a torn Achilles tendon.
Smyly was born in Gainesville, Georgia, about an hour's drive north of Atlanta, and grew up a Braves fan. He said the team was at the top of his list when he became a free agent.
"They are such a young, energetic team with a ton of talent,'' he said. "It's a team that's just built to win. Once I became a free agent, I was interested in the Braves right away. Once they expressed interest in me, it made my decision kind of easy.''
The Braves hope to get more out of Smyly than they did from Cole Hamels, who signed a one-year $18 million deal for 2020 that wound up as $6,666,667 prorated. He pitched one game because of injuries and missed the entire playoffs.
Atlanta also had to deal with former All-Star Mike Foltynewicz suffering a mysterious drop in velocity that resulted in him being farmed out after making only one start.
Despite their starting pitching woes, the Braves won their third straight NL East title and reached the league championship series, losing in seven games to the eventual World Series champion Los Angeles Dodgers after squandering a 3-1 lead.
The Associated Press contributed to this report.