The well-preserved wreck of the 412ft steel-hulled ship was found by Odyssey this summer, nearly 4,700 metres below the inhospitable waters of the North Atlantic.
The vessel had settled on the seabed in a fully upright position, with the cargo holds open and the bullion accessible via the hatches, using remote-controlled robotic submarines.
The Gairsoppa was carrying seven million ounces - about 200 tonnes - of silver to help to fund the war effort, sailing from Calcutta to Liverpool, via Freetown in Sierra Leone - an important staging point for the convoys.
Under a contract with the Department of Transport, which inherited responsibility for the ship, Odyssey will be permitted to retain 80 per cent of the value of the silver in return for taking on the commercial risk and expense of locating the Gairsoppa. If it brings all the bullion to the surface when the planned recovery begins next summer, it will make the company about £118m.
Andrew Craig, the senior project manager, said: "We've accomplished the first phase - the location and identification of the target shipwreck - and now we're hard at work planning for the recovery phase."
The bullion was a mixture of privately owned silver insured by the British Government and state-owned coins and ingots. Researchers working for Odyssey have used the Gairsoppa's cargo manifest and documents from Lloyd's War Losses Register, which detail an insurance payout, to establish the amount of silver on board.
Odyssey is currently locked in a court battle with Spain over the ownership of 500,000 silver coins recovered close to the remains of a vessel claimed by Madrid and has previously attracted criticism from archaeologists who argue that historical ship wrecks should be left untouched.
The company insists its work is done to stringent archaeological standards and helps to preserve knowledge that would otherwise be lost.