Dudek, who will be the stand-in for Spanish international goalkeeper Iker Casillas, was officially presented after passing his medical.

The 34-year-old will earn 1.5 million euros (2 million dollars) a year, according to press reports.

Dudek becomes Real's fourth signing this summer after German defender Christoph Metzelder (Borussia Dortmund), Brazilian defender Pepe (FC Porto) and Argentine striker Javier Saviola, who is out of contract with Barcelona.

Dudek arrived in Liverpool in 2001 and was the hero of their Champions League final victory in 2005, when they beat AC Milan on penalties.

But last season his relationship with coach Rafael Benitez has been strained as he has found himself second in the pecking order behind Spaniard Pepe Reina.

Dudek is just the third Polish-born footballer to play at Real after W. Rozitsky from 1913-1915 and Raymond Kopa (Kopaszewski) in the 1950s.