Ryan, 33, had appeared in 25 games this season, posting a 1-1 record with just two saves and an ERA of 6.53. The 6'5 lefty was on the disabled list from April 23 to May 15 with tightness in his left trapezius.
Fans had grown impatient with Ryan, who struggled in finishing off games and lost his job as a closing reliever.
General manager J.P. Ricciardi said he cut Ryan because the team simply didn't believe he would become effective again. "No, we didn't," Ricciardi said Wednesday. "He was not going to be our closer, we didn't foresee him being our closer next year. It's our job to make professional evaluations and from the player we evaluated to sign to the player we have now, it's two totally different guys, and we just don't think he's going to be the pitcher he was when we signed him."
Downs, meanwhile, now in his sixth season in Toronto, had been on the DL with a left toe sprain since June 18. Downs is 1-0 with eight saves and a 1.98 ERA in 26 games this season.
The 33-year-old has a 15-10 record with 15 saves and a 3.14 ERA in 258 career games with the Jays.