Cleveland designated outfielder Jhonkensy Noel for assignment to clear space on the roster.
Bruihl, 28, was designated for assignment himself when the Blue Jays signed reliever Tyler Rogers.
He tossed 13.2 innings in 15 appearances for the Blue Jays last season with a 5.27 ERA.
The southpaw was also on Toronto’s post-season roster for its American League Division Series win over the New York Yankees, allowing two runs in just 0.1 of an inning’s work.
Noel, 24, batted just .162 last season with six home runs and 13 RBIs in 69 games.
