The application for the 63-hectare garden will now be referred to the Secretary of State because it is being built on the green belt, on the site of a former historic garden at Worsley New Hall.
An RHS spokesperson said the decision meant that the "exciting and inspirational project" had passed another key stage.
RHS Bridgewater is a joint venture between the RHS, Peel Land and Property and Salford City Council, which agreed to fund it to the tune of £19 million in December 2015.
The design, by landscape architect Tom Stuart-Smith and Manchester architects Hodder and Partners, will include the development of a new Welcome Building, demonstration and teaching allotments, a shop and café, an events and learning space, a new glasshouse and school of horticulture, and the restoration of the historic Walled Garden and its existing accompanying buildings.
The RHS originally hoped that work could start on site by this spring with the aim of opening the 4ha Walled Garden to the public in June 2019.
Marcus Chilton-Jones will be the curator. Once complete it will join Wisley in Surrey, Rosemoor in Devon, Hyde Hall in Essex, and Harlow Carr in North Yorkshire. The RHS hopes to see visitor numbers reach between 600,000-700,000 by 2029 and says an estimated 140 direct and 180 indirect jobs will be created.