The process to move the embassy began under President George W. Bush, but the deal was completed during the Obama administration.
Trump had been expected to combine a ceremonial opening for the new building - a distinctive glassy cube - with an official visit at the invitation of Prime Minister Theresa May.
Trump is scared of facing mass protests if he comes.
The British government has extended Trump an invitation for a state visit.
Khan said Trump "would without doubt have been met by mass peaceful protests" if he hadn't canceled the trip.
Mr Trump accepted the Queen's invitation for an official state visit when the prime minister met him past year.
Some British lawmakers questioned whether Trump would be welcome after he re-tweeted videos from a far-right British group and criticized London Mayor Sadiq Khan following a terror attack previous year.
London Mayor Sadiq Khan has now responded saying that Trump "got the message" from Londoners, and alluded that Trump's real reason for cancellation is fear of protests - something that has been widely speculated.
Moves to relocate the embassy to the new site began in October 2008 because of security concerns after a report on the old embassy's perimeter security in June 2007.
Although his coming to the United Kingdom would not have been the state visit previously promised by Theresa May, it had been expected to see thousands of Brits take to the streets in protest against his policies.
President Trump fired off a series of critical tweets over Khan's handling of the attack, mocking the mayor's comments that there was "no reason to be alarmed" over armed police on the streets. The building was sold in 2009 to a Qatari government investment fund, which plans to turn it into a hotel.
US President Donald Trump and Britain's Prime Minister Theresa May wait at the start of the first working session of the G20 meeting in Hamburg, Germany, July 7, 2017.