The application to restore Chiswick House & Gardens was granted full planning permission by Hounslow Council's Sustainable Development Committee.
Proposals include restoring historic vistas by remodelling the landscape, demolishing the existing 1950s cafe and erecting a contemporary design in its place, as well as restoring the conservatory and providing a site for a marquee for corporate events.
Objections received from local residents during the consultation period focused on plans to fell hundreds of trees. Since the public consultation, the number of trees to be felled has been reduced from more than 400 to 350. Certain veteran trees, including the weeping willow next to the cafe, have been saved by public protest.
Despite protests against the plans, the council passed the application from the Chiswick House & Gardens Trust, submitted on behalf of site custodians English Heritage and Hounslow Council.
The committee accepted the argument given for felling the trees - to return the landscape to the naturalistic style designed in the 1720s by Lord Burlington and William Kent - which ensures it is a landscape registered by English Heritage. A total of 1,600 trees will be planted during the restoration.
Project director Martin Clayton said: 'We are delighted the application has been successful. A huge amount of work went into drawing up the proposals for regenerating the gardens by the Chiswick House & Gardens Trust, with a great deal of invaluable input from a range of groups and local people. All this hard work has finally paid off."
The decision whether to grant the £7.9m Heritage Lottery Fund money earmarked for the restoration will be given at the end of the month and, if successful, work on the project will start in April.