The approval follows the backing earlier this year of the borough of Wandsworth on the south side of the river.
The Greater London Authority must give final consent. If it is approved and funding is secured, it is hoped that construction could begin next winter.
Palace Investments plans to create the 170m-long Diamond Jubilee Bridge to connect Imperial Wharf and Chelsea Harbour to Battersea on the south side of the Thames.
The scheme design is led by architect Chris Medland of local firm One-World Design. The design team includes Expedition Engineering, Beckett Rankine, RPS environmental consultants, Thompson Ecology and Oxford Archaeology.
The bridge will be made up of three spans with a design of three arches. Original plans submitted to the council in October last year, showed the bridge connected to the existing Grade II* listed Cremorne Railway Bridge – better known as Battersea Railway Bridge. However, following objections from English Heritage, the scheme has been modified. Now the plan is for two new river piers to be erected so that the Jubilee Bridge would stand adjacent to the railway bridge, rather than be attached to it.