The agreement, which will begin next season, will see the Puma brand on all of the club's team kit, training gear, equipment and replica strips. The value of the deal has not been revealed.
Puma is one of the world's top lifestyle brands. It replaces current supplier Umbro.
Charles Green said: "Rangers and Puma are massive global brands and this relationship will undoubtedly improve the distribution of club merchandise in the UK and overseas."