The airport will be shut all day and all flights cancelled, affecting up to 16,000 passengers, a spokeswoman said.
The bomb was discovered at about 05:00 GMT on Sunday at George V Dock during pre-planned work at the airport in east London, the Met Police said.
The airport was shut at 22:00 and the Met said it was working with the Royal Navy to remove the device.
According to the airport's website, a total of 261 arrivals and departures were scheduled for Monday - with 130 flights having cancelled by 08:00 GMT.
Passengers have been told not to travel to the airport as the terminal is closed and to contact their airline.
Robert Sinclair, CEO of the airport, apologised and said: "I recognise this is causing inconvenience for our passengers, and in particular some of our local residents.