Davies went 1-9 with a 6.75 ERA in 13 starts for Kansas City this season. The 27-year-old was a fourth-round pick in the 2001 First-Year Player Draft.
The native of Decatur, Ga., is 43-65 with a 5.59 ERA in 151 career games -- 144 of which he started. His best season came in 2008 when he went 9-7 with a 4.06 ERA.
Toronto also announced on Sunday that left-hander Trever Miller was unconditionally released. The 38-year-old veteran appeared in six games for the Blue Jays this season and allowed two runs in 3 2/3 innings.
Miller was designated for assignment by the club on Aug. 26 after he surrendered an eighth-inning solo home run in Seattle.