The Spanish giants will move from the Vicente Calderon, their home for 50 years, to the new stadium to be renamed Wanda Metropolitano after their sponsors Chinese property company Dalian Wanda Group.
Wanda have had ties with Atletico since January 2015 when it acquired 20 percent of the club.
“The payment will be made in three annual installments, for a total of 30,422,520 euros, with interest,” a spokesman for Madrid Town Hall said.
“In addition the club will take over the access work, for a total of 29.875 million euros and the construction of 4,000 public parking spaces.”
La Peineta — also known as the Madrid Olympic Stadium — was originally built to host athletics, and was renovated with a view to Madrid’s failed bids to host the Olympic Games in 2012 and 2016.
Built in 1904 its capacity will be increased from 20,000 to 73,000.
The new ground’s name is also a reference to the club’s first real stadium, the Metropolitano, where they played their first La Liga games before moving to the Vicente Calderon in the south of the city in 1966.
The Vicente Calderon, which hosts the Copa del Rey final on May 27, will be destroyed after the La Liga side have vacated the premises at the end of the season.