MADRID (AFP) - Lyon announced on Wednesday the transfer of their France international Karim Benzema to Real Madrid for between 35 million and 41 million euros.

The deal was reached after Real agreed to up its offer from 32 million euros, the sports newspaper Marca said on its Internet site.

Radio Cadena Ser said Benzema will sign a six-year contract with the Spanish giants.

This is the fourth signing by Real under the new presidency of "Galacticos" president Florentino Perez, after Brazilian midfielder Kaka, Portuguese winger Cristiano Ronaldo and Spanish defender Raul Albiol.

After Kaka was presented to fans at the Bernabeu stadium on Tuesday evening, Perez told Spanish radio that the next signing would be announced "today or tomorrow."

Real are looking for a striker and have been keen on Benzema since negotiations broke down with Valencia for Spanish international David Villa.

The former France and Real star Zinedine Zidane, who is now a senior advisor at the club had recommended Benzema to Perez, Spanish media said.

Benzema has played at the seven-time French champions since 2004, where he was top scorer in the French league in 2007 and 2008.

Lyon said last week that it wanted to keep him for another year.

Real also has its eye on another France international, Bayern Munich midfielder Franck Ribery.