The Rays have 10 days to trade, release or waive Mohr.
Dohmann, 29, will make his Rays debut. He made 36 relief appearances for the Bulls, going 4-1 with five saves and a 2.08 ERA, holding opponents to a .211 batting average. He has not surrendered a run over his last 11 1/3 innings.
Ryu, 24, will make his second tour with the Rays. He made his first Opening Day roster this season and appeared in 15 games out of the bullpen, going 1-1 with a 5.06 ERA, 11 strikeouts and nine walks before he was optioned to Durham on June 2.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.