(CNN) -- Lyon have accepted an offer of approximately 35 million euros ($50m) from Real Madrid for 21-year-old French international striker Karim Benzema.
Benzema will become Real Madrid's fourth signing of the summer, taking their spending to 200m euros.
The French side confirmed on their official Web site that the fee, which could rise to 41 million euros with performance clauses, has been agreed and the player now has permission to discuss personal terms with the Spanish giants.
A statement read: "Lyon announce they have reached an agreement with Real Madrid on the details of the transfer of their international striker Karim Benzema. Latest transfer gossip and rumors
"A few days ago Karim Benzema informed club president Jean Michel Aulas of his desire to move to the Madrid club, which has been his favorite club after Lyon, earlier than he had foreseen.
"The player wanted to seize the opportunity which Real Madrid offered him to be one of the major elements in their new ambitious project based around the greatest players of the world.
"Lyon accepted Karim Benzema's decision and negotiated the conditions of a transfer which satisfies all the different parties. The club wishes Karim the greatest success with Real Madrid."
Spanish radio station Cadena Ser said Benzema will sign a six-year contract to become Madrid's fourth signing of the summer after Kaka, Cristiano Ronaldo and Valencia defender Raul Albiol.
Real had been looking for a striker all summer and set their sights on Benzema, on the recommendation of Zinedine Zidane, when a deal to sign David Villa collapsed.
Benzema came through the ranks with Lyon and burst onto the scene in the 2007-08 season with 31 goals in 51 games, a streak that saw him named Ligue One player of the year as well as topping the league's scoring charts.
The last campaign was less impressive for both club and player, as Lyon failed to win the French title for the first time in eight years, but Benzema nevertheless scored 23 goals in all competitions -- an average of a goal every other game.
The deal will take Madrid's summer spending to over $280 million since Florentino Perez returned as club president.