Bradford, who was acquired from the Orioles on Thursday, is expected to join the team on Saturday. The veteran Reyes was told he had been designated for assignment after Friday night's 5-3 win over the Mariners.
"It's not easy, and we had to choose somebody and we chose him right now," Rays manager Joe Maddon said. "I just told him, last year we were not very good and we would have been horrid had he not been here. And I wanted him to know how much I personally appreciated what he had done. I felt like we had a good relationship, and we're going to miss him. You keep moving things along, and you're always trying to make yourself better and we have. We had to choose somebody, and it was him."
Reyes, 38, has endured two stints on the disabled list this season while going 2-2 with a 4.37 ERA in 26 appearances. Last season Reyes led the team with 26 saves.
"I wish all the luck to the team," Reyes said. "Hope they make the right move. I move on and see what happens the last couple of months."
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.