Nick DePaula of ESPN reported the news.
Green, 31, posted a video of a puma on Instagram on Monday, hinting at the move. He averaged 8.6 points and 3.6 rebounds last season. No terms of the agreement have been made available.
Signing Green could be a precursor to bringing in Raptors teammate Kawhi Leonard, who is a shoe free agent. Many thought the brand was hinting at signing Leonard with a post that ultimately was meant for Green.
Puma has made major strides in expanding its basketball brand over the last year. The company signed Deandre Ayton, Marvin Bagley III and Michael Porter Jr. during the draft period. It also took on DeMarcus Cousins this week.
Green isn't a major name who is going to sell shoes, but he's a respected veteran who might wind up luring the biggest shoe free agent along with him.