Art dealer John Martin is leading the project to redevelop the Grade II listed terrace of five townhouses into art galleries and exhibition space.
At a meeting last night the council approved the scheme, subject to planning obligations called section 106 agreements.
Martin said: “This is testament to the landlords and the council who have seized this business opportunity. Galleries are finding it tougher to find space in central London. But this is evidence there are landlords and councils who see the value in having galleries.”
A council spokesman said: "Planning permission was granted, subject to a legal agreement to be completed by March 31."
A number of art industry figures backed the plans including Nic McElhatton, chairman of Christie’s South Kensington, the Society of London Art Dealers and Russia’s Hermitage Museum.
The scheme, called Cromwell Place, will include offices, viewing rooms, art storage and 16 exhibition spaces varying in size at up to 3000 square feet.
Applications for membership will be available in May and if it gets planning permission it hopes to open by 2019.
The project is a joint venture between Martin, property advisers CWM, and South Kensington Estates, which owns the properties. Consultant Gerald Eve is managing the planning process.