Asked what his advice was for Brexit, the US president - who promised a "very big trade deal" with the UK - said: "He needs no advice, he is the right man for the job."
He added: "I've been saying that for a long time, it didn't make your predecessor very happy, but I've been saying it for a long time."
Mr Johnson responded: "You're on message there."
Meanwhile, the Prime Minister said he has made it clear the NHS is off the table when it comes to trade talks with the US, adding there is an agreement on that with Mr Trump.
Mr Johnson said: "Not only have I made clear of that, the president has made that very, very clear. There is complete unanimity on that point."
Mr Trump said the two countries would have a "very big trade deal", adding it would be "bigger than we've ever had with the UK."
He said: "They won't have the anchor around their ankle."
He continued that they could make a trade deal "very quickly" and the US "don't anticipate any problems" because they are "no longer stymied by the other side."
"This is a different person," Mr Trump said. "this is going to be a person who is going to make a great Prime Minister in my opinion."
Mr Trump added that US allies "respected" the trade war with China because it "has to happen".
The latest developments came as shadow Brexit secretary Sir Keir Starmer said he could use a parliamentary device to compel ministers to release documents linked to the Operation Yellowhammer no-deal preparations.
It means Mr Johnson's government could be forced to publish the latest assessments of the possible impact of a no-deal Brexit when Parliament returns.
In a letter to Michael Gove, the Cabinet minister in charge of no-deal planning, Sir Keir indicates Labour could use a humble address to the Queen - a tactic the opposition has used in the past to require the government to disclose Brexit-related documents.
Sir Keir said Labour would "not hesitate to use all parliamentary devices available" when Parliament resumes on September 3 to compel ministers to publish all the Operation Yellowhammer documents if the government does not do so voluntarily, the Sunday Times reported.
Leaked Operation Yellowhammer documents indicated the UK will be hit with a three-month "meltdown" at its ports, a hard Irish border and shortages of food and medicine after it leaves the EU without a deal.
In his letter, Sir Keir disputes Mr Gove's claims last week that the leaked -documents were out of date and outlined a "worst-case scenario".
He said: "You challenged the claim that these anticipated effects of leaving the EU without a withdrawal agreement represented the government's understanding of the base 'most likely' scenario and intimated the information was nevertheless out of date.
"However, the government have not provided up-to-date information or explained what their assessment of the most likely effects is."
The Prime Minister has reportedly taken legal advice from attorney general Geoffrey Cox about temporarily shutting down Parliament - known as prorogation - for five weeks from September 9.
The Observer reported that the move would allow for a Queen's Speech, starting a new parliamentary session, on October 14.
Such a move would keep MPs away from the Commons until shortly before the European Council summit of EU leaders on October 17, potentially preventing moves to block a no-deal Brexit.
Government sources said Number 10 officials ask for legal and policy advice every day.
But a source added: "The claim that the government is considering proroguing parliament in September in order to stop MPs debating Brexit is entirely false."
Further details have emerged about the government's public information campaign about a potential no-deal Brexit.
The Cabinet Office is in the final stages of signing off the major media blitz to support businesses and the public, which will give information about what will be required for any scenario on October 31.
The campaign will feature TV and radio adverts, billboards, social media and a dedicated gov.uk website providing advice and information.
A fast and simple "60-second checker" on gov.uk is promised, which will help businesses and UK and EU citizens work out what, if anything, they need to do.
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Meanwhile, business secretary Andrea Leadsom said businesses wanted Britain to "crack on" and leave the European Union to put an end to uncertainty.
Writing in The Sunday Telegraph, she said many firms were "overwhelmingly positive" about the future.
"I want businesses to see a team in the heart of Whitehall that's helping them to get the best out of Brexit - talking up their trade at every opportunity," she said.
"Brexit is a once-in-a-generation chance," she added. "I believe that Britain's best years for business and for all our people lie ahead."