The council, which owns the site, is looking for a developer to buy the land and is understood to be in talks with Zog Group.
A deal would pave the way to complete the final phase of the west London scheme at New Wharf Gardens with 434 new homes.
The plans involve demolishing an existing school buildings and erecting five buildings of between 11 and 17 storeys.
Westminster Council planning and city development committee chairman Alastair Moss said: “The standard of the plans and the light it affords to the neighbourhood despite the density of the scheme get it well over the line.
“The quality of the housing is particularly strong and the designs set a high bar for the site.”