Morrow gets $4 million this year and $8 million in each of the following two seasons. Toronto has a $10 million option for 2015 with a $1 million buyout.
The 27-year-old Morrow was 11-11 last season with a 4.72 ERA.
But the right-hander also set career highs in wins (11), innings (179 1/3) and strikeouts (203).
On Monday, the Jays announced the signing of 44-year-old infielder Omar Vizquel to a minor league contract.