Moran agreed Monday with Atlanta on a minor-league contract and received an invitation to MLB spring training, Chris Harris of the Mississippi Braves reports.
Moran cleared waivers Thursday and was outrighted to Triple-A Salt Lake.
Moran was designated for assignment by the Angels on Monday.
Moran had his contract selected by the Angels on Sunday.
Moran will serve as a non-roster invitee for the Angels during spring training in 2022.
The Rays reassigned Moran to their minor-league camp Monday, Neil Solondz of the Rays Radio Network reports.
Moran signed with the Rays as a non-roster invitee Thursday, Marc Topkin of the Tampa Bay Times reports.
Moran (kneecap) was reinstated from the 10-day injured list and outrighted to Triple-A Wichita on Wednesday, but he refused the assignment and was released by the Marlins, Jordan McPherson of the Miami Herald reports.
Moran was placed on the 10-day injured list Tuesday with right knee patella tendinitis.
Moran was recalled from the Marlins' alternate training site Saturday.