The developers plan to transform the Grade II-listed Former Covered Market into a new five-screen Picturehouse cinema, cafés, bars and restaurants.
Buildings on Plumstead Road will be demolished ahead of a planned construction start in 2023.
Surrounding land in Woolwich will be built out to provide 800 homes in a multi-building scheme that will rise to 15, 17 and 18 storeys, with two 23-storey blocks.