The club hopes work on the project, which would see a striking new exterior added and include a hotel and a shopping centre, can begin after the end of this season and be completed by 2017, Spanish media reported.
Half the financing would come from selling naming rights and half from a bond issue among Real members, meaning the club would not need additional bank loans, Sport24 quoted the reports, as saying.
By remodelling the Bernabeu, which was opened in the 1950s and reworked for the 1982 World Cup, Real are looking to increase match day revenue, one of their key income streams.
To win the project, Hamburg-based GMP beat off competition from three other bidders, reports said.
Real Madrid's ace rivals, Barcelona , has also decided to go ahead with a remodelling of the Nou Camp stadium.
Barcelona members, who collectively own the Catalan club, will be given a chance at the beginning of April to vote on the proposal that would increase the capacity of Europe's biggest stadium from 98 000 to 105 000 and help boost match day revenue. (ANI )