The 81,000-capacity venue will be fitted with a retractable roof and will also include room for a shopping centre and possibly a hotel, all of which is to be enveloped inside a metallic, undulating facade.
A mall that is currently adjacent to the stadium will be knocked down and replaced by a large public garden.
The city hall tweeted that its executive council had approved the project, which will be financed by Abu Dhabi-based sponsor IPIC, who will be given naming rights.
The original plan involved enlarging the stadium plot onto public land to build a hotel and shopping centre.
But it was blocked by Madrid's High Court in 2015 on the grounds that the European Commission was investigating the club over an alleged overpriced land transfer between Real Madrid and the city.
In July 2016, the Commission found that the transfer had indeed been overvalued and constituted illegal state aid.
That autumn, the club returned a total of €20.3 million ($23 million) to Madrid city council over the land deal and tax breaks the EU said were giving it unfair advantages.
In the new project, which was unveiled around the same time, the shopping centre will now be included within the existing stadium.
Take a tour of the new Bernabeu. pic.twitter.com/xABMisnk8l
— GЯP I_ΛM_MΛDЯID (@I_AM_MADRID) May 31, 2017
It is still unclear whether it will also feature a hotel.
The original structure was inaugurated in 1947 before being renamed in 1955 after former club president Santiago Bernabeu, who died in 1978.
It has already undergone several makeovers since the 1982 World Cup in Spain.
Real's great domestic rivals Barcelona have also announced plans to remodel their Camp Nou ground.
Real's cross-city rivals Atletico Madrid are for their part due to move to a new 70,000-seat stadium this year, leaving behind the 55,000-capacity Vicente Calderon stadium, which is set to be demolished and turned into a park and housing.