Part of the Docklands Light Railway has been suspended and some roads remain closed, Transport for London have said.
He said that any passengers expecting to fly to or from the airport today should contact their airline for further information.
The airport authorities have urged all passengers to avoid travelling to the facility, through a Twitter post.
The unexploded WWII bomb was found at George V Dock, North Woolwich, just after 5am yesterday.
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"Specialist officers and the Royal Navy have attended and confirmed the nature of the device".
The ordnance was found in the River Thames at the George V Dock during pre-planned works at the airport. "Passengers are advised not to travel to the airport until further notice", the statement continued.
As per the Metropolitan Police, this discovery was made at dawn on Sunday.
A 214-metre exclusion zone has been implemented to ensure that the bomb can be safely dealt with.
The ordnance was discovered during planned development work at the airport. Now let's hope the situation is dealt with immediately & the public doesn't suffer.