Video report by ITV News Washington Correspondent Robert Moore
Dame Karen Pierce, currently the UK permanent representative to the United Nations, will become the first woman to hold the post, Downing Street said.
She replaces Sir Kim Darroch, who was forced to stand down last year after diplomatic cables he wrote criticising the Trump White House were leaked to the press.
Her appointment comes amid reports that the president was “apoplectic” at Mr Johnson’s decision last week to give Huawei a role in building the UK’s 5G network.
The Financial Times reported that British officials were taken aback by the force of Mr Trump’s language when the Prime Minister telephoned to explain the move.
It followed intensive lobbying from Washington that allowing a Chinese supplier access to the country’s critical communications networks would constitute a major security risk.
US officials repeatedly warned that they would withhold intelligence-sharing from any ally which did so.
Downing Street refused to be drawn directly on the report, insisting that the relationship with the US remained “excellent”. However there was no direct denial of the claims.
Asked about the call, a No 10 spokesman referred to a statement issued at the time highlighting Mr Johnson’s comments on the need for liked-minded countries to work together “to diversify the market and break the dominance of a small number of companies”.
The spokesman expressed confidence that intelligence-sharing with the US and other allies in the Five Eyes partnership – Australia, Canada and New Zealand – would continue as in the past.
“We have been clear that this will in no way inhibit our ability to share intelligence with other countries including Five Eyes partners,” he said.
However, media reports from Australia claimed that Foreign Secretary Dominic Raab – who is on a visit to the country – came under fire over the decision when he met MPs on Australia’s parliamentary intelligence committee in Canberra on Thursday.
The Sydney Morning Herald reported that he was confronted by one member who told him: “How would you feel if the Russians laid down infrastructure in your own networks? That’s how we feel about Huawei,”
There was no immediate response from No 10 or the Foreign Office.
But the claims add to the sense that Dame Karen – one of Britain’s most senior diplomats – may have her work cut out when she takes up her new role once her appointment is formally approved by the Americans.
As well as the differences over Huawei, the two countries are at odds over the UK’s plan to impose a tax on US tech giants, with the Americans threatening to retaliate with tariffs on the UK car industry.
The UK is also pressing for the extradition of the wife of a US intelligence official charged with causing the death of 19-year-old motorcyclist Harry Dunn, whom the Americans are refusing to hand over.
At the same time, the Government in London is anxious to secure an early post-Brexit free trade deal with the US now that the UK has formally left the EU.
Asked if Dame Karen would be tasked with repairing relations with Washington, the No 10 spokesman said: “The UK has an excellent relationship with the United States and I think Dame Karen’s ability as a diplomat is proven by her career.”
In a statement, Dame Karen said: “I am honoured to have been asked to represent the UK in the US.
“I think it is the UK’s single most important relationship. There is a deep bond between Britain and the US, built on many pillars.”