Sources with knowledge of the signing say the contract is a multiyear deal that comes with a guarantee of at least $2 million annually.
Wiggins wore adidas during his only year of college ball at the University of Kansas.
Adidas was pressured to try to secure its future even further with Wiggins in part because Rose, the company's highest-paid NBA spokesman, has missed nearly two seasons with injuries.
The company recently re-signed Portland Trail Blazers guard Damian Lillard to an extension that could last for the next 10 seasons, and they added Dante Exum, who was taken fifth overall by the Utah Jazz in this year's draft.
Adidas has a long way to go to catch up to Nike, which owns an astounding 95 percent of the basketball shoe market share (Jordan: 58 percent; Nike: 37 percent) in the United States, according to market retail tracking firm SportsOneSource. Adidas has a 3 percent share.