Ken Rosenthal was the first to report the news on Twitter.
Granderson reportedly agreed to a US$5 million contract pending a physical.
Granderson has played 14 seasons in the Major League Baseball.
The changes will be in place for the Jays' home opener against the New York Yankees on March 29.
The 36-year-old veteran figures to slot in one of Toronto's corner outfield positions.
While he was on the Dodgers' roster for both the NLDS and NLCS, he was left off of the World Series roster as he had only been able to muster one hit between the two postseason series. And the Blue Jays look to be willing to bet he has more left to contribute. However, he did pop 26 home runs and still draws plenty of walks.
He has hit.252 with 319 homers and 865 RBIs over 14 seasons.
Early in his career, Granderson spoke of former Jays centre fielder Vernon Wells as a role model, He even felt heat from the Tigers' fan base after he warned Wells about some tricky spots in the Comerica Park outfield. He has played there consistently over the past several seasons.