He said the new embassy was a "signal to the world that this special relationship that we have is stronger and is going to grow and get better".
"Reason I canceled my trip to London is that I am not a big fan of the Obama Administration having sold perhaps the best located and finest embassy in London for "peanuts", only to build a new one in an off location for 1.2 billion dollars", Trump wrote.
Mr Trump also criticised the location of the new building in Vauxhall, south London, as an "off location", adding: "Wanted me to cut ribbon-NO!"
In 2008, when George W. Bush was president, the United States signed a conditional agreement to acquire a site for the construction of a new embassy in the Nine Elms area of Wandsworth, southwest London.
The American flag was this month removed from the US embassy in Grosvenor Square as part of the move to a location on the South Bank in a $1 billion construction project.
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".
The White House says that President Donald Trump's tweet canceling a trip to London was in reference to a visit for the opening of the new USA embassy and that efforts to schedule a later state visit continue.
A Trump visit has been on the cards since British Prime Minister Theresa May visited the United States a few days after Trump's inauguration previous year.
Even Trump's biggest supporters suggested that protests played a role in his decision not to visit. In December, Ambassador Woody Johnson said he was looking forward to welcoming the president when he visited.
Trump tweeted overnight that he would not attend the ceremony, initially scheduled for next month.
A spokesman for May's Downing Street office said the invitation for the state visit "has been extended and accepted".
Yet, while President Trump's opponents were gleeful and the police relieved that they would not have to mount a security operation like no other, the fragile state of UK-US relations should be a wider source of concern.
But British officials have been dismayed by some of Trump's pronouncements, particularly a proposed ban on Muslims entering the United States and most recently when Trump rebuked May on Twitter after she criticized him for retweeting British far-right anti-Islam videos.
Despite the president publicly blaming predecessor Barack Obama, the U.S. embassy said the plan to finance the project was developed in 2007, at a time when George W Bush was in the White House.
The exchange prompted further calls to dump the visit.
"It appears that President Trump got the message from the many Londoners who love and admire America and Americans but find his policies and actions the polar opposite of our city's values of inclusion, diversity and tolerance", Khan said in a statement.
"His visit next month would without doubt have been met by mass peaceful protests". He said the opening of the embassy was a matter for the U.S. government.