Cecil was 2-3 last season with five saves and a 2.70 earned-run average in 66 appearances.
The 28-year-old has spent his entire major-league career with the Blue Jays after joining the team in 2009.
He was an all-star in 2013 when he went 5-1 with a 2.82 ERA and 70 strikeouts over 60 relief appearances.
Earlier Thursday, the Blue Jays signed outfielder Andy Dirks to a minor-league contract with an invite to major-league spring training.
Dirks, 28, was originally claimed from Detroit on Oct. 31 and became a free agent when he non-tendered on Dec. 2.
He spent parts of three seasons with the Tigers after making his major-league debut in 2011. Dirks was hampered by back and hamstring injuries last year.
In 297 career major-league games, Dirks has a .276 average with 24 homers and 100 RBIs.