The London Borough of Wandsworth initially granted outline consent for the development in June 2012.
The redevelopment forms part of the Vauxhall Nine Elms Battersea opportunity area regeneration initiative.
Following the appointment of a development partner in January 2013, a revised application was submitted.
The latest approval grants outline consent for the wider project and detailed consent for the redevelopment of the market and for a 54-storey residential tower in the development’s Northern Site.
Overall, the revised plans would see the construction of 3,000 new homes, around 12,500 square metres office space and around 9,200 square metres of retail, leisure and new community facilities, including shops, cafés and restaurants.
The 3,000 new homes is an increase from the 2,500 planned in the original outline consent.
A planning report on the latest application said the scheme would "aim to provide 600 affordable units (299 affordable rent and 301 intermediate) which equates to 20.2 per cent on a unit basis and 18.3 per cent by floor space assuming 2,971 residential units".
2,971 residential units is the minimum residential figure if the maximum office floorspace proposed is provided.
But the report added that "a 20 per cent affordable housing figure generates a funding deficit that both the applicant and the council are committed to resolving ... However, should this deficit not be overcome the applicant has committed to providing at least 446 affordable units".
A planning report for the 2012 application, said 15 per cent (around 375) of the proposed homes would be affordable.
The 2014 planning report concluded that overall, the development "is considered to be largely in line with the vision for the [Vauxhall Nine Elms Battersea opportunity area] and includes a S106 offer that provides a well balanced package offering acceptable mitigation to the affects of the development, a reasonable level of affordable housing, and a considerable CIL payment contribution towards providing sustainable development across the opportunity area as a whole including transport and social infrastructure requirements".
Other projects being undertaken in the Nine Elms area include the building of the new United States Embassy and the redevelopment of Battersea Power Station.