Mr Tuttle said the current embassy would be available for sale almost immediately, as long as the move was approved by US Congress and planning authorities in Britain.
He said the announcement was only the start of a “multi-year, multi-stage” process which could take up to five years.
The current embassy was always an oddity in the US diplomatic set-up because of the lease arrangement with the Duke of Westminster – virtually every other major mission is owned outright by the US.
The Duke reportedly said he would only sell if the US government returned his family’s land, confiscated during the American War of Independence.
His property company the Grosvenor Group refused to comment on the move.
American links with the square date back to the 1780s when John Adams lived in London before becoming US president.
The embassy has been there since 1938 and moved into the present nine-storey building – with its distinctive golden eagle on the roof – in 1960.
Its central location made it an obvious target for its detractors and in 1968 the square had to be closed because of the strength of protest over the Vietnam war.
Trump also criticised the Obama administration of selling the current site for “peanuts”. “Bad deal,” he added.
Although we don’t know how much the current site was sold for when it was flogged to the Qatari sovereign wealth fund in 2009, experts estimated it was worth as much as £500m – but that was before it was given its Grade II listing.
The current site is also the one of the few US embassies in the world to which the US does not own the freehold. A report by the LA Times in the 1980s suggested back in the 1940s, the second Duke of Westminster, whose Grosvenor Estate owns the freehold, was asked to hand it over to the US government. He responded by insisting he would only give it up if the US returned 1,200 acres of prime Florida real estate which had been confiscated after US independence. It politely declined.