Comcast SportsNet's Evan Drellich first reported the Red Sox were going to acquire Davis, but it was being kept under wraps for now because Oakland's game on Wednesday against the Baltimore Orioles was in extra innings.
The Red Sox officially announced the deal sending minor league outfielder Rafael Rincones to Oakland in exchange for Davis after the A's lost 8-7 to the Orioles.
Rincones is 18 years old and currently plays in the Dominican Summer League with a .258/.373/.369 slash line and 13 doubles in 198 at-bats.
Davis brings outfield versatility to the Red Sox. He has played all three outfield spots for the A's this season, and he remains a threat on the bases with 26 stolen bases in 32 attempts.
The 36-year-old hasn't done much with his bat in 2017, though, entering Wednesday with a .233/.294/.353 slash line in 300 at-bats. Even with Bradley's injury, Boston isn't lacking outfield depth as Andrew Benintendi, Mookie Betts, Chris Young and Brock Holt can rotate positions.
Davis could be used as by the Red Sox as a spot starter in September and a pinch-runner late in games during the regular season and for a potential playoff run.