The 26-year-old has spent his entire career at his home-town club but has only made a handful of first-team appearances for the Spanish giants.
Three of those came last season when then-coach Jose Mourinho caused a major stir by dropping long-serving club captain Iker Casillas and replacing him with back-up Adan.
Madrid then signed Diego Lopez during the January transfer window and Adan found himself falling back down the pecking order.
A club statement on Monday read: "Real Madrid and Antonio Adan have rescinded the contract which tied the player to the club. Real Madrid are grateful for his professionalism and his affection for the club, and wish him all the best in his next step."