The Serie A club, controlled by US investors, said Nike will produce all its playing and training kit in a deal that will start from 2014-15.
The Romans traditionally play in red and yellow. They will wear an unbranded kit next season after dropping current supplier Kappa in a legal dispute over alleged quality and distribution issues.
"AS Roma is committed to becoming the premier football club in the world, on and off the field," Roma CEO Italo Zanzi said. "This partnership is a fundamental step in that mission," he added.
Roma have a long way to go to meet that ambitious target. They are currently seventh in Italy's 20-team Serie A and last won the league in 2001.
The club have plans to move to a new stadium and last month gave a prospective Middle Eastern investor a deadline of Thursday, March 14, to show he has the funds needed to take a stake in the club.
Roma named Sheikh Adnan Adel Aref al Qaddumi as the prospective new backer of the club.
Nike, the world's largest sportswear company, already has kit supply deals in Italy with champions Juventus and Inter Milan.