The proposed scheme, which has towers of 14, 21 and 28 storeys, replaces Eastbury House, a 1958 office building on the south bank of the Thames.
Construction is expected to start early next year, once the existing building has been demolished and the site cleared.
Rogers Stirk Harbour and Partners designed the tripartite building for Berkeley subsidiary St James, which has been praised by Design Council Cabe as a “well-proportioned building of pleasing dimensions”.
The scheme on London’s South Bank is located within the Vauxhall Nine Elms Battersea Opportunity Area, which features the US Embassy project and the Battersea Power Station redevelopment.
In the area, Richard Rogers’ firm is working on plans for a mixed-use tower for Foxtons founder Jon Hunt on a nearby Texaco garage site.