The 21-year-old has signed a five-year contract with the Spanish giants.
Real Madrid wrote on their Twitter: “Real Madrid C.F. & Málaga C. F. have reached an agreement for the transfer of Isco who will play for the Whites for the next 5 seasons.”
New Manchester City boss Manuel Pellegrini was keen to bring the youngster to Eastlands.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
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