The 26-year-old has spent five seasons in the big leagues, most recently with the Yankees after starting the 2011 campaign in Seattle. He was drafted by, and spent the first four years of his career with, the Indians.
Last season, Laffey was 3-2 with a 3.88 ERA in 47 relief appearances. He held left-handed hitters to a .242 average. He has made 49 starts in his career and owns a lifetime 4.34 ERA.
The Blue Jays also announced they have signed the following four Minor League free agents with invitations to Spring Training: right-hander Jerry Gil, right-hander Garrett Mock, right-hander Robert Coello and shortstop Brian Bocock.