Donald Trump says Boris Johnson is the “right man for the job” of delivering Brexit.
The US president hailed the new British prime minister at the G7 summit in Biarritz, France, on Sunday.
Mr Trump promised a “very big trade deal” between the two nations after the UK no longer has the EU “anchor around their ankle”.
The US president claimed his long held admiration for Mr Johnson had rankled with previous prime minister Theresa May, saying it “didn’t make your predecessor very happy”.
The two leaders met at the summit to talk about the possibility of a UK-US trade deal once Britain has left the European Union.
Mr Trump said: "We're going to do a very big trade deal, bigger than we've ever had with the UK and now at some point they won't have the obstacle, they won't have the anchor around their ankle, because that's what they have."
However, Mr Johnson has warned that a trade deal with the US will not be "plain sailing" and has raised a series of areas where he wants concessions from Washington.
He told Mr Trump: "Talking of the anchor, Donald, what we want is for our ships to take freight, say, from New York to Boston, which for the moment they're not able to do."
The president said he wanted a deal done "quickly" because in the past he had been "stymied" under Mrs May and while the UK was still negotiating Brexit.
He added: "This is a different person and this is a person that's going to be a great Prime Minister, in my opinion. He's going to be a fantastic Prime Minister, I can tell you".
Mr Trump said Mr Johnson was the "right man for the job" of handling Brexit, adding: "I've been saying that for a long time. It didn't make your predecessor very happy."
Mr Johnson told him: "I know that there will be some tough talks ahead because at the moment I don't think we sell a single joint of British lamb in the United States; we don't sell any beef… and there are huge opportunities for the UK to penetrate the American market in ways we currently don't."
Asked if he had made clear his views on protecting the NHS and animal welfare standards in trade talks with Mr Trump, the Prime Minister said: "There is complete unanimity on that point."
The Prime Minister also warned Mr Trump against escalating his trade war with China.
"We are in favour of trade peace on the whole," he said as the two leaders and their teams had a working breakfast at the Hotel du Palais, where there was a menu of scrambled eggs and veal sausages.
The two leaders agreed to set up a working group focused on closer economic links.
US director of the National Economic Council Larry Kudlow and UK Cabinet Secretary Sir Mark Sedwill have been directed to set up the special relationship economic working group (SREWG).
"The SREWG will develop market-oriented principles for economic growth and increase bilateral co-operation on issues related to the modern 21st-century economy," the White House and Number 10 said in a joint statement.
The statement said that during the talks in Biarritz the two leaders discussed how Brexit presented opportunities for "deepening our already robust economic and commercial relationship, including a comprehensive trade agreement".
Mr Johnson is also due to have talks at the G7 with European Council president Donald Tusk.
Reports suggested Mr Johnson will tell Mr Tusk that the UK will only hand over a fraction of the £39 billion divorce bill agreed by Mrs May if there is no Brexit deal.
Mr Johnson ordered government lawyers to calculate how much of the bill the UK is liable to pay and they concluded it could be as little as £7 billion, the Sunday Times and Mail on Sunday reported.