Benzema was also reported to be a target of Manchester United
Real Madrid have reached an agreement to sign striker Karim Benzema from French side Lyon, subject to the 21-year-old passing a medical.
The Spanish club will pay an initial £30m for the France international, a figure that could rise to £35m if performance-related clauses are met.
"Benzema will have his medical in the next few days," said a Real statement.
Benzema, who will sign a six-year-deal at the Bernabeu, had been linked with a move to Manchester United.
Real have already signed forwards Cristiano Ronaldo, Kaka and defender Raul Albiol for a combined £148m this summer.
Former France and Real Madrid great Zinedine Zidane, who is now a senior advisor at the Spanish club, is believed to have recommended Benzema to club president Florentino Perez after negotiations to sign David Villa from Valencia broke down.
"A few days ago Karim Benzema informed the club president Jean Michel Aulas of his desire to move to the Madrid club, which had always been his favourite club after Lyon, earlier than he had foreseen," said a statement on the French club's website.
"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."
Benzema joined Lyon's youth academy at the age of nine and progressed through club's ranks before making his first-team debut aged 17.
He scored 31 goals in 51 games during the 2007-08 season to finish top scorer in Ligue 1.
Benzema scored 23 goals in all competitions last season but could not prevent Lyon ending the season without league title for the first time in eight years.
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