New York received cash considerations as part of the deal.
Carrasco only pitched in eight games (six starts) this season for the Yankees, tossing a 5.91 earned run average after giving up 21 runs and 39 hits in 32 innings.
The 38-year-old veteran was doing well in Triple-A this season with a 3.27 ERA in 11 games (10 starts), posting a 4-2 record.
Carrasco signed a one-year deal worth $5 million at the beginning of the season and will now be joining his fourth team in three years.
The Venezuelan spent the first 11 years of his career as a member of the Cleveland Guardians. In 2017, Carrasco led the league with 18 wins en route to placing fourth in the American League Cy Young voting, posting a career-best (as a starter) with a 3.29 ERA.
Carrasco is in the waning years of his career, but the 44-60 Braves will look to revive his career one last time as the team will make their final back-end push as the season begins to close.