Lyon said on its website that Madrid will pay a minimum fee of €35 million ($NZ77 million), rising to up to €41 million euros with performance bonuses.
"Lyon has accepted Karim Benzema's decision and has negotiated the terms of a transfer which satisfies all sides," Lyon said in a statement. "The club wishes Karim the best of success with Real Madrid."
The Spanish club headed off stiff competition from Manchester United to secure a deal for the 21-year-old Benzema, considered one of the most exciting young players in Europe.
He becomes Madrid's third major signing under its ambitious president Florentino Perez.
Madrid has already bought midfielder Kaka from AC Milan, winger Cristiano Ronaldo from United - and also defender Raul Albiol from Valencia. Madrid spent a record 80 million pounds ($NZ207 million) on Ronaldo.
"The player wishes to take the opportunity offered to him by Real Madrid to become one of the key players in an ambitious new policy involving several of the world's biggest players," Lyon said.
Perez has vowed to bring success back to Madrid after returning to the presidency in June. Last season, fierce rival Barcelona won the Spanish domestic double and the Champions League.
Benzema first hinted at a move away from the seven-time French champion in November, saying he wanted to discuss his future with club president Jean-Michel Aulas when the season ended.
"There are a lot of clubs, Barca, Real, but also Manchester United, Milan. They are all big clubs you dream about," Benzema told L'Equipe TV at the time. "I want to progress at the highest level to be among the world's best."
A prolific scorer in Lyon's youth team, Benzema broke into the first team during the 2004-05 season.
He scored more than 30 goals in the 2007-08 season but failed to make an impact at the 2008 European Championship in a lackluster French team which went out in the group stages without winning a match. Benzema was annoyed by coach Raymond Domenech's decision not to pick him against the Netherlands in a match Les Bleus lost 4-1.
Benzema has a prolific strike rate in the Champions League, scoring 12 goals in just 19 games.
Last season, Lyon could not sustain its bid for an eighth straight title and finished third behind Marseille and new champion Bordeaux.
Having tied Benzema down to a long-term deal until 2013, Aulas fully anticipated Benzema's value on the transfer market.
Benzema's burgeoning reputation as a goalscorer was magnified even further after he scored a brilliant individual goal against Manchester United at Stade Gerland in the Champions League two seasons ago.
A good negotiator in the transfer market, Aulas sold midfielders Michael Essien to Chelsea at the start of the 2005-06 season and Mahamadou Diarra to Real Madrid the following season.
