The 500kg device was found in the water at King George V Dock during the early hours of Sunday (February 11) and Metropolitan Police enforced a 700ft security cordon shortly after its discovery.
At around 6pm on Monday, the fused device was removed from its original position to a second location within the dock, a police spokesman said.
A new exclusion zone was enforced and residents were evacuated from their homes and taken to temporary emergency accommodation in the early evening.
London City Airport, which was shut following the discovery, has since reopened.
On Tuesday (February 13), the Royal Navy said it would be transporting the device from the seabed to a secure area to carry out a controlled explosion.
Lieutenant Commander Jonny Campbell, the officer in charge of Southern Diving Unit 2, said the Royal Navy's priority is “safety to life” during the operation.
He said: “We are taking the necessary steps to ensure the device is as safe as possible before we remove it from the seabed and tow it away to a safe disposal site.
“We will then attach high-grade military explosives before carrying out a controlled explosion. The aim is to cause as little disruption to the city of London as possible.”
Around 9,000 of passengers at London City Airport had flights cancelled or diverted after the bomb was discovered while the exclusion zone remains in place.
Robert Sinclair, chief executive of the airport, urged passengers due to fly on Monday (February 12) not to come to the airport and to contact their airline.
The transportation of the bomb, a 500kg tapered end shell measuring around 1.5 metres, will impact river traffic and motorists have been advised that bridges along the route will be temporarily closed.
A Met Police spokesman added: “While every effort is being made to progress the operation as quickly as possible, it is important that the necessary steps and precautions are taken to ensure it is dealt with safely.
“We would again like to thank everyone affected for their patience and cooperation.”
Keep up to date with the latest news in west London via the free getwestlondon app.
You can set up your app to see all the latest news and events from your area, plus receive push notifications for breaking news.