Dudek, who was released by previous club Liverpool earlier this year, has been brought in by Real to provide competition to Spain international Iker Casillas, and he joins Pepe, Christoph Metzelder and Javier Saviola as new arrivals at the Bernabeu.
Real doctor Alfonso Del Corral said of the Polish goalkeeper following his medical: "He is 34 years old but his physical shape is as good as any young player. He is an athlete."
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