On Monday, the Twins got their man after acquiring the 31-year-old along with catcher Anthony Recker and cash considerations from Atlanta in exchange for minor league right-hander Huascar Ynoa.
Ken Rosenthal of FOX Sports reported that the Twins assumed the remainder of Garcia's salary (approximately $4.55 million) and $200,000 of Recker's $300,000 salary. The Braves are sending $100,000 to the Twins.
Garcia, who is making $11.5 million this year, will be a free agent after the season.
He owns a 4-7 mark with a 4.30 ERA in 18 starts with Atlanta in 2017. Garcia has posted a 66-52 record with a 3.65 ERA in 176 career appearances (165 starts) with the St. Louis Cardinals and Braves.
The Braves acquired Garcia in December from the Cardinals for right-hander John Gant and two minor-leaguers.
Recker is batting .223 with four homers in 41 games this season for Triple-A Gwinnett. The 33-year-old is hitting .199 with 18 homers and 70 RBIs in 206 career contests with the Oakland Athletics, Chicago Cubs, New York Mets and Braves.
Ynoa, 19, has recorded a 5-11 mark with a 3.05 ERA in 30 starts with rookie-level Elizabethon and the Gulf Coast League Twins.