Toronto received Roach on Tuesday, and he will join Triple-A Buffalo later this week.
Roach was designated for assignment Sunday after going 2-4 with a 6.00 ERA in seven starts for Triple-A Louisville.
Outfielder Michael Saunders was transferred from the 15-day disabled list to the 60-day DL to make room on the 40-man roster. Saunders is out for the season with a bone bruise in his left knee.
Roach gave up eight hits and four runs in 3 1/3 innings in his only major league start this season, for the Chicago Cubs. He had a 4.75 ERA in 16 games for San Diego last season.