The application has been referred to the GLA (Greater London Authority) and the GOL (Government Office for London). The Richmond Council should receive their response within the next two months.
RFU Chief Executive, Francis Baron, said he was delighted with the outcome after much work by consultants and the RFU's Stadium and Community Relations departments.
The South Swatted development, the final phase in the rebuilding of Twickenham, will increase the seating capacity by 7,500 to 82,000.
The new building will include a 200-bedroom, four-star hotel, a new shop, offices, another restaurant, a leisure club, a conference and exhibition centre, basement parking for 200 cars and a new ticket sales facility. It also involves the building of two blocks comprising 24 flats, with new access on to Rugby Road. New ticket gates and perimeter fencing will also be provided.
The leader of the Richmond Council, Tony Arbour, said: "This exciting scheme is of national and international importance as the stadium is the home of English rugby, a showpiece ground which focuses the eyes of the rugby world.
"The redevelopment will ensure it becomes truly fit for the world champions. It will also have major economic spin-offs for west London, providing a massive boost for employment and the economy of the region as a whole."
The development is expected to take two years to complete.