The London Borough of Bexley approved the plans, submitted by housing association Peabody, at a meeting yesterday.
The suite of planning applications included a detailed application for the first phase of the regeneration scheme, Southmere Village, which would include 525 new homes - around 230 of which will be affordable - a new library and commercial space for cafes, retail businesses and local enterprises.
This would be centred around a new public square on the banks of Southmere lake.
The future phases, submitted in outline form, would deliver just over 1,000 new homes, new commercial and community spaces at Binsey Walk, Coralline Walk and Sedgemere Road. They would be linked by a new pedestrian and cycling route between Abbey Wood station and Southmere Lake.
A planning report into the detailed application said that the proposal was "compliant with national, London wide and borough wide policy documents given that the area has long been identified as being in need of regeneration".
It said that the overall development would "provide an opportunity for Abbey Wood and South Thamesmead to be reborn with an iconic development" and "provide a place to live for existing residents and new people that they will be proud of and rebrand Thamesmead as a brand new community in the heart of south-east London for the 21st Century".
The document said that Peabody’s aspiration is to provide "at least" 35 per cent, or 591 homes as affordable housing across the overarching development.
The report said that, in the detailed application, Peabody proposed to provide 235 affordable homes, representing 45 per cent of the total number of homes, due to the need to rehouse tenants from buildings due to be demolished elsewhere in Thamesmead.
A spokesman for Peabody confirmed that all existing tenants affected by the redevelopments would be re-housed in line with their existing tenancy agreements.
Peabody said it hopes the development will be built in four phases, with Southmere Village due to start in 2017 and the final phase anticipated to be completed in 2024.