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.
It's the first No. 1 overall draft pick adidas has signed since signing Chicago Bulls guard Derrick Rose in 2008.
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 also shifted Washington Wizards guard John Wall from its Reebok brand to its main adidas brand last year and will be debuting a signature shoe this upcoming season.
The other high-profile name in the draft coveted by all the shoe companies was Duke's Jabari Parker, who was taken by the Milwaukee Bucks with the second pick. Parker signed with Nike's Jordan brand.
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.