The £70m project will improves access to the theatre complex and creates a new café, a rooftop garden and a workshop.
The Brutalist concrete building was famously damned by the Prince of Wales who described it as a “clever way of building a nuclear power station in the middle of London without anyone complaining”.
Work is due to start by early 2012, provided funding can be raised for the facelift.
A spokesperson for the National Theatre said: “Fundraising will now begin in earnest. It is a challenging time to raise money, but we believe that the combination of our commitment to the National Theatre’s future and the generosity and the vision of our supporters, will enable this vital project to proceed.
“The scheme is both sensitive and transformational. Haworth Tompkins’ designs display deep respect for Denys Lasdun’s building.”