The move was announced it October 2008, when George W. Bush was president.
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.
British MPs have repeatedly called for the offer of a state visit for Mr Trump to be withdrawn, following his crackdown on immigration from majority-Muslim countries and promotion of far-right group Britain First on Twitter.
Late Thursday night, the president revealed why he canceled a trip to London to open the new embassy there.
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But asked earlier about the prospect of Trump's visit, Johnson said he was looking forward to it, adding: "I think he will be very impressed with this building and the people who occupy it".
Many Londoners have made it clear that Donald Trump is not welcome here while he is pursuing such a divisive agenda.
Sections of the United Kingdom media claim that the visit was cancelled amid fears of mass protests as the embassy's plan to move from Mayfair to Nine Elms in London pre-dated the Barack Obama administration and was first reported in October 2008, when George W Bush was still the president. But Trump gave a different reason, blaming former President Obama.
With Downing Street not commenting on the matter, the Liberal Democrats welcomed the news.
But many commentators believe Trump was instead put off by the prospect of significant protests during his visit with the potential for disruption, negative publicity and embarrassment as the real reason for his continuing avoidance of the UK.
The President was not due to meet the Queen until a full state visit at a later date, and a second source said the lack of "bells and whistles" and royal involvement next month visit may have discouraged him.