The building work is set to take place between May 2017 and February 2021 at an estimated cost of €600 million.
A new stadium will have a roof over all sections, with the surrounding areas also set to be renovated as part of the plans.
"It was a difficult decision," president Sandro Rosell said.
"The two projects were very attractive but we were committed to put to a referendum a project that was viable from a technical, urban-planning and economic perspective.
"The Nou Camp is part of our collective memory, the biggest stadium in Europe and an icon of the city of Barcelona.
"The option of building a new stadium on a new site has been rejected as the final cost could have saddled the club and its members with debt and tied the hands of future boards of directors.
"To maintain our status as leaders we have to take this historic step which will require effort from everyone involved.
"We will increase the value of our real estate and the capacity to generate additional income without having to sell off assets."
