The first containers salvaged from the stricken vessel, the MSC Napoli, are due to arrive at Portland Port in Dorset.
A shuttle barge, carrying about 70 containers, is travelling from the ship's beached position in Lyme Bay.
About 80% of the ship's fuel oil has been removed and salvors expect to remove all of it by the weekend.
The Napoli was deliberately grounded on Saturday 20 January amid fears it would sink in deep water.
Two specialist cranes are being installed at the docks in Dorset in order to unload the large steel crates.
Salvors have been working round the clock to remove the ship's 3,500 tonnes of fuel oil at rate of about 20 tonnes an hour.
The operation to remove the containers, which started on Monday, has been helped by calm seas.
Salvors held by harnesses on board the heavily-listing Napoli have been working to secure containers to the crane mounted on a lifting platform called Big Foot.
Removing the rest of the containers and transporting them to Portland by barge is expected to take up to five months, depending on the weather.
The 275m (900ft), Napoli was carrying more than 2,000 containers, of which 103 went overboard.
The beaching of about 50 containers at Branscombe, east Devon, led to two days of looting before police cordoned off the area.
South African newspapers are reporting that Volkswagen has shut down its car production plant for one day a week after 130 containers of parts needed for the production of four models were lost.
South African wine producers also fear problems, as dozens of oak barrels needed for the February grape harvest were lost.
Julia Gosling of the Maritime and Coastguard Agency (MCA) told BBC News: "We are very pleased with the rate of removal of oil, it has been exceptional.
"Removal of the containers has been steady.
"It's a precarious job for those on board who have to hook up the containers and if the weather deteriorated we would have to stop."
Devon County Council leader Brian Greenslade confirmed the council would be holding a public inquiry into the beaching.
The move comes amid questions about the decision to take the Napoli to an area of protected World Heritage Site coastline.
The Napoli was being towed to Portland when its deteriorating condition prompted the beaching at Lyme Bay.
But local MP Adrian Sanders has raised questions about why the Napoli had not originally been taken to Falmouth or France.
MSC NAPOLI SALVAGE OPERATION
The Napoli's containers will be unloaded from the stern first by crane barge Big Foot
A second crane on Big Foot will then transfer containers to shuttle barge Boa Barge 21
Shuttle barge will then transfer containers to Portland Harbour, where they will be offloaded
Lightering vessel Forth Fisher is positioned on the other side of the ship pumping off its remaining fuel oil
A decision will be made over whether to re-float the ship after all the oil and containers have been removed
Oil is being pumped off at a rate of approx. 20 tonnes per hour