Upton’s first full season with Tampa Bay was 2007, when he hit a career-best .300 with 24 homers and 22 stolen bases. His home run totals have increased in each of the last three seasons, but he has hit below .250 with more than 150 strikeouts in four straight years.
Bourn was the Braves’ leadoff hitter, but Upton is not expected to fill that role.
Elsewhere, the Boston Red Sox made a flurry of minor moves, trading right-handers Zach Stewart and Sandy Rosario as well as third baseman Danny Valencia.
Stewart was sent to Pittsburgh and Rosario to Oakland for players to be named. Valencia was shipped to Baltimore for cash.
Boston also hired Greg Colbrunn as hitting coach.
Athletics reliever Pat Neshek agreed to a one-year contract that avoided salary arbitration, while Kansas City traded right-hander Vin Mazzaro and first baseman Clint Robinson to the Pirates for minor league pitchers Luis Santos and Luis Rico.
The Chicago Cubs designated right-hander Casey Coleman for assignment to make roster room for newcomer Scott Feldman, who agreed to a $6 million, one-year contract the previous day.
Feldman’s former team, the Texas Rangers, acquired right-hander Cory Burns from San Diego for a player to be named or cash.
AP Sports Writers Charles Odum, Greg Beacham and Joe Kay contributed to this report.