The 33-year-old outfielder has reportedly signed a two-year deal worth in the range of $9-10 million with Detroit.
Last season with Toronto, Davis batted .268 with six homers, 24 RBIs and 45 stolen bases in 331 at-bats.
In November, the Jays declined to give Davis a qualifying offer.
Davis, who bats right-handed, was acquired by the Jays from Oakland prior to the 2011 season in exchange for Trystan Magnuson and Daniel Farquhar.
He also had stints with the Pittsburgh Pirates and the San Francisco Giants.
For his career, Davis has 27 homers, 224 RBIs and 268 stolen bases.