The project - part funded by a £7.9m Heritage Lottery Fund grant - is the result of four years of fundraising and two years of work on site.
Local campaigners previously protested against the removal of 400 trees to open up vistas at the west London site.
However, the scheme also includes the planting of more than 1,600 trees, including trees propagated from the original 18th century cedars of Lebanon.
In addition, the project restored a 19th century conservatory that housed a rare collection of Camellias, the planting of native trees and shrubs in the Northern Wilderness and the restoration of the Walled Gardens, which will be open to the public on special days.
The restoration of the gardens was also funded by English Heritage, the London Borough of Hounslow, the Wolfson Foundation, the Garfield Weston Foundation and the Monument Trust, with additional support from other individuals and organisations.
Architects Caruso St John have designed a new cafe within the grounds that has already been open since February. Scott Wilson was appointed to provide detailed design through to implementation.