A statement on the club's official website reads: "Real Madrid and former Bayern Munich player Hamit Altintop have reached an agreement in which he will join the club for the next four seasons."
The Turkish 28-year-old midfielder leaves Bayern after four years with the Bundesliga side.
Altintop's departure had been expected after the German club confirmed he was leaving following their final game against Stuttgart last week, with his deal set to expire in June.
On Saturday the former Schalke man told Goal.com he would be playing his football away from Germany.
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