The deal isn't expected to be announced until Wednesday when NBA teams can officially sign players after the league's moratorium on player business and next season's salary cap is set.
Hansbrough became a unrestricted free agent when the Indiana Pacers opted not to re-sign the 27-year-old after four seasons with the club.
The University of North Carolina product was drafted by the Pacers 13th overall in 2009. He averaged 8.9 points and 4.7 rebounds over those four years. In 2012-13 Hansbrough averaged seven points and 4.6 rebounds.
Toronto is looking to bolster its front court after dealing Italian forward Andrea Bargnani to the New York Knicks for perimeter shooter Steve Novak, 39-year-old centre Marcus Camby and draft picks.
Hansbrough made US$3.055 million last season with the Pacers.