The 36-year-old right-hander was 5-3 with a 2.45 ERA and 37 saves in 43 chances for Cincinnati last season, reaching 30 saves for the seventh time. He held batters to a .198 average, the lowest of his career.
Cordero, a three-time All-Star, has a 44-45 record with a 3.17 ERA and 327 saves, 12th on the career list. He is expected to fill the setup role for closer Sergio Santos, acquired in December from the Chicago White Sox.
"I've got no problem with that because I've been a setup guy in the past," Cordero said during a telephone conference call. "Being a closer for a long time, I know what to do. I've got to just treat the eighth inning like it's the ninth inning. I've just got to go out and do my job and pass it on to Santos in the ninth inning."
Cordero said he has added some pitches to his repertoire and doesn't always rely on his fastball, as he did earlier in his career.
"For the last few years I've been learning how to pitch in and out, moving the ball a lot better, throwing a lot of sinkers," Cordero said.
He said he had interest from a few teams this offseason but Toronto was the best fit.
"I've seen the Blue Jays play. I know they've got a great offense every time," Cordero said. "It's just a matter of time before they put everything together. It's going to be fun."
To make room on the 40-man roster, the Blue Jays designated outfielder Darin Mastroianni for assignment.