The Turkey international is set to make the move to his homeland after failing to impress at the Bernabeu last season.
Altintop appeared just nine times for the Primera Liga champions after joining from Bayern Munich on a free transfer last summer, signing a four-year deal.
He announced at the end of May he had agreed a move to Galatasaray and the Turkish outfit confirmed the deal on Friday.
A statement on the club's official website said: "We have reached an agreement for four seasons with Real Madrid player Hamit Altintop, starting from 2012-2013 season."
Reports suggest Galatasaray will pay the Spanish giants €3.5million for Altintop, whose twin brother Halil plays in the Super Lig for Trabzonspor.
It will mark the first time the German-born midfielder has played for a Turkish club.
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