Trump said on Twitter he canceled the visit because the US embassy's former location was sold at a "bad deal".
On Friday night, a spokesman for the US embassy said: "The US chancery in Grosvenor Square had aged beyond its ability to be improved to current security and life safety standards without extensive investment in infrastructure that would require appropriated dollars".
Just south of the River Thames, the cube-shaped embassy building is in sight of Westminster and part of a £15 billion, 561-acre regeneration project set to transform one of the South Bank's last remaining industrial stretches.
Many Londoners have made it clear that Donald Trump is not welcome here while he is pursuing such a divisive agenda.
Mr Khan had said the United States president had "got the message" from Londoners and would have been met by "mass peaceful protests" if he went ahead with plans to open the new embassy. "Wanted me to cut ribbon-NO!"
The US will leave behind an imposing 1960 stone and concrete embassy in London's upmarket Grosvenor Square - an area known as "Little America" during World War Two, when the square also housed the military headquarters of General Dwight D Eisenhower.
Since then, however, the president has indicated he does not want to take up the invitation if he is going to face mass demonstrations and it had been expected he could make a low-key working visit rather than a trip which involved all the trappings of a state occasion.
The spokesman added: "A state visit (invitation) has been extended and accepted and we will confirm the details in due course".
European Central Bank looks to review stimulus duration
As a result, the Australian Dollar to Euro (AUD/EUR) exchange rate dropped back to near the week's opening levels of 0.6544. The pan-European FTSEurofirst 300 index rose 0.23 percent, and MSCI's gauge of stocks across the globe gained 0.66 percent.
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 past year. But Foreign Secretary Boris Johnson blamed Khan and Labour Party leader Jeremy Corbyn for discouraging the US leader from coming.
He noted how Mr Trump would have been met by "mass peaceful protests".
British Foreign Secretary Boris Johnson said opponents such as Khan were putting the relationship with the United States, the biggest investor in Britain, at risk.
In the meantime, the relationship between May and Trump has come under strain.
"We will not allow US-UK relations to be endangered by some puffed-up, pompous popinjay in City Hall", Johnson tweeted. "He is not welcome in London and he certainly isn't welcome in Queenstown", he said. It will be open for business on January 16.
In 2009, the Obama State Department agreed to sell the Grosvenor Square building where the US embassy was located to the Qatar royal family.
"He has been to countries all over the world and yet he has not been to the one with whom he is closest", former UKIP leader Nigel Farage, a Trump ally, told the BBC.
But Stephen Doughty, an opposition Labour lawmaker, tweeted: "We are not a big fan of his racist, sexist, unthinking behaviour".