"Lyon announce they have reached an agreement with Real Madrid on the details of the transfer of their international attacker Karim Benzema," said a statement on the Lyon website.
The French giants revealed that the 21-year-old's desire prompted them to accept the offer from Madrid.
Benzema will be Real's fourth big star signing, after the club brought in Kaka, Cristiano Ronaldo and Spanish international defender Raul Albiol.
The four deals take Real's spending spree to more than 200 million Euros since the re-election of Florentino Perez as chairman on June 1st.
Real turned their attention to signing Benzema after they failed to convince Valencia officials of letting Spain forward David Villa join the royal club.
Benzema, who played 26 times for France, scored 66 goals for Lyon over a period of five seasons he spent at the club's first team.