Toronto announced the moves before Wednesday night's game against Tampa Bay.
Ryan has struggled this season, going 1-1 with a 6.53 ERA in 25 relief appearances. The left-hander allowed 22 hits, including five homers, and 17 walks over 20 2/3 innings.
"It was one of those things with Downs coming back and us needing to make a move, he was the 12th guy on the staff right now, it's probably best for both parties," Toronto assistant general manager Alex Anthopoulos said. "A few days ago I think you saw in the media that he expressed some frustration of not being able to pitch more and be used more. We couldn't get him the work that he wanted."
Ryan had mainly been used recently in blowout games. The 33-year old is in the fourth year of a $47 million, five-year contract.
"He was a pro," Anthopoulos said of Ryan's reaction to the decision. "He understood. It's never a fun thing to do. It's never a fun day, but we thanked him for the years he had been here. He has a chance to move with his career, hopefully latch on with a team that can maybe give him more of an opportunity to pitch more meaningful innings."
Ryan wasn't the same after undergoing left elbow ligament replacement surgery in 2007. He did have 32 saves last year with a 2.95 ERA.
"I wouldn't say it was a mistake," Anthopoulos said of Ryan's contract. "I think it's unfortunate he got hurt. The one thing you can never predict is health."
Downs had been sidelined sine June 17 by a left big toe injury.
Toronto manager Cito Gaston said Downs will probably return to his closer's role immediately.