The three-phase regeneration of the 1930s Peabody estate will raise the number of homes from 353 to 599.
Sisk built over 150 hones in phase one, with phase 2 providing 200 affordable homes and a new community centre.
There will be 109 social rented homes, 54 extra care homes, and 35 offered for shared ownership to help people on to the housing ladder.
Designed by architect Hawkins Brown, the new homes and community centre are due to complete in 2022.
The £87m phase also features a wild garden, a play area and a central public square for the community to enjoy.
Energy-efficiency measures include photovoltaic panels and a district heating system, contributing to Wandsworth council’s aspiration to be a carbon neutral borough by 2030.
Tom Williamson, senior development manager at Peabody said: “More top quality, sustainable and affordable homes are three years away at St John’s Hill and will be a great addition to this part of London.
“Like Phase 1, the brick design incorporates detailing and public artwork, creating unique and distinct buildings of the highest quality. There will be more open space, gardens and trees than before, and the new community centre will be a hub for local people to gather.”
Ajaz Shafi, Managing Director of John Sisk & Son’s Southern business division said: “We expect to be on site later this year and will be working hard to ensure we deliver this development to the highest standards in collaboration with our supply chain partners by 2022.”