Plans for the new £500m ground will see the current stadium demolished.
A club statement said: “We are grateful that planning permission was granted for the redevelopment of our historic home.
“The committee decision does not mean that work can begin on site.
“This is just the latest step, although a significant one, that we have to take before we can commence work, including obtaining various other permissions.”
The new stadium has been designed by architects Herzog and de Meuron and construction work is expected to last three years.