The scheme designed by Haworth Tompkins with Industrial Architect Ashton Smith will be delivered in several phases.
The 13ha site will be developed with a major long-term storage building, engineering education hub, double storey warehouse, and boatyard and pier.
Contractors will also restore full public access to the island.
The approval paves the way for site enabling works, demolition, utility diversions, installation of a pedestrian bridge and river wall works.
Technical design work for the first buildings is now underway, with an anticipated start on site in 2022.