The goalkeeper's contract with the Santiago Bernabeu side has been terminated with immediate effect
Adan is a product of the Madrid youth academy and made his official first team debut in the 4-0 Champions League win over Auxerre in December 2010.
Despite having a rare, brief run in the starting XI under former coach Jose Mourinho last season, Adan was largely a peripheral figure at the club and was therefore keen to leave Madrid.
"Real Madrid CF and Antonio Adan have terminated the contract that linked the player to the club," a statement on the club's official website reads.
"Real Madrid would like to thank him for his professionalism and his love for the club and wish him luck for the future."
Adan made 18 official appearances for Madrid during his time at the club.