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The official Lyon website confirmed the deal had taken place before the Spanish club was able to do so.
21-year-old Benzema, who is a French international, has agreed a six-year contract with Real Madrid and will cost 35 million Euros, plus a further six depending on incentives.
He is Real Madrid's fourth signing of the summer, joining Kaka, who was presented to the press and public on Tuesday evening, Cristiano Ronaldo and defender Raul Albiol, who will be presented on Thursday.
Benzema's arrival takes the club's summer spending since Florentino Perez returned as club President on June 1, to around 215 million Euros.
It is expected that in the coming weeks Real Madrid will spend more money on a central midfielder and a defender, expected to be Liverpool's Xabi Alonso and Alvaro Arbeloa.
The club could also be in the market for a central defender as well as a left back.
Perez has said another player would be signed in the near future, when he appeared on Spanish radio station Cadena Ser in the early hours of Wednesday morning. However, Benzema's arrival comes as a surprise as it was thought he was close to joining English Premier League champions Manchester United.