Morales, 33, batted .263 with 30 homers and 93 RBIs for the Kansas City Royals. It was the second 30-homer season of Morales' career.
Toronto targeted the switch-hitting Cuban after negotiations with Encarnacion began to break down. Encarnacion is reportedly seeking a five-year, $125 million deal after matching his career high of 42 homers and setting a career best with 127 RBIs.
Morales is the first free agent to sign with a new team this offseason.
Also on Friday, the Blue Jays signed Cuban infielder Lourdes Gurriel Jr. to a seven-year, $22 million deal, according to reports.
The 23-year-old Gurriel defected from Cuba along with his older brother during the Caribbean Series in the Dominican Republic in February.
His brother, 32-year-old Yulieski Gurriel, signed a five-year, $48 million deal with the Houston Astros in July, and he hit .262 with three home runs and 15 RBIs in 36 games this season.
Lourdes Gurriel, who also played for the Havana Industriales before defecting, was declared a free agent in August. He had a .321 batting average with eight homers and 32 RBIs in 43 games.