Toronto also outrighted catcher Brian Jeroloman and right-hander Drew Carpenter to Triple-A Las Vegas. The moves mean the club now has 40 players on its 40-man roster.
Hoey went 1-2 with a 5.47 ERA in 26 games for Minnesota last season. He also posted a 1-3 record with a 3.83 ERA and nine saves with Triple-A Rochester.
"He's a guy that some of our scouts like and thought we should take a chance on," Blue Jays general manager Alex Anthopoulos said. "[He's] a guy with arm strength that has a developing split and a solid slider, and we'll see if we can get the most out of him.
"But really, it was a low-risk move, and we've been pretty aggressive this winter claiming guys on waivers to try to continue and build that depth."
The 28-year-old Hoey is 4-7 with a 7.02 ERA in 61 career games at the big league level. He was selected by the Orioles in the 13th round of the 2003 First-Year Player Draft, and he was later traded from Baltimore to Minnesota as part of the deal for J.J. Hardy.
Hoey, who is 6-foot-6 and 210 pounds, is expected to compete for a spot in the bullpen during Spring Training if he remains with the club. Hoey also has one option left on his contract and could be sent down to the Minor Leagues without first being exposed to waivers.
The Blue Jays are rebuilding their relief corps after Frank Francisco and Jon Rauch left via free agency, and right-hander Shaun Camp is expected to follow suit.