It will be his first visit to Britain since he was elected in 2016. He had been due to open the new US Embassy in London in February but cancelled the trip.
Theresa May’s spokesman said the US President will hold bilateral talks with the Prime Minister, with further details to be “set out in due course”.
On Wednesday, Sky’s senior political correspondent Beth Rigby revealed that Mr Trump would make the trip in mid-July, with a full announcement expected within a day or so.
In Washington, White House press secretary Sarah Huckabee Sanders confirmed to reporters that the date had been set.
The trip is only being billed as a “flying visit” rather than an official state one, which would have seen Mr Trump hosted by the Queen.
But the US leader will still reportedly meet Her Majesty on the 24-hour trip, which will follow a NATO summit.
The visit will be held predominantly outside London, amid the fear of protests, The Telegraph reported.
The newspaper said Mr Trump will stay overnight and hold talks with Mrs May at her countryside retreat of Chequers.
Mr Trump had been urged earlier to stay away from London because there is a risk of “major protests, crime and disorder”.
In a letter, six conservative groups who support the US President suggested he visit his “ancestral home” of Scotland instead.
Foreign Secretary Boris Johnson hailed the “fantastic” news of Mr Trump’s visit.
“Looking forward to seeing our closest ally and friend on the GREATest visit ever,” he wrote in a post on Twitter.
But London Mayor Sadiq Khan, whom Mr Trump criticised for his response to the London Bridge terror attack, said if the President visits the capital he “will experience an open and diverse city that has always chosen unity over division and hope over fear”.
Mr Khan added: “He will also no doubt see that Londoners hold their liberal values of freedom of speech very dear.”
Liberal Democrat deputy leader Jo Swinson has urged that the “scaled down trip not be met with scaled down protests”.
“Protesting against a man with dangerous, misogynistic and racist views is our responsibility,” she said.
“It is our opportunity to stand in solidarity with all the people he has abused and denigrated.”
Mr Trump was due to open the new US Embassy in London in February, but cancelled after saying the building was too expensive – and tweeted that he was not a “big fan” of the decision to move its location.
However, it is thought he scrapped the visit over fears of mass protests in the capital, something that is also believed to have played a part in the postponement of a state visit.
Number 10 insisted before the “working visit” announcement that the state visit invitation, which would entail lavish ceremonies and an audience at Buckingham Palace, still stood.
His trip to the UK will come some 15 months after Mrs May visited the White House in January 2017 – the first world leader to do so following his inauguration.
It will also coincide with the second anniversary of Mrs May becoming Prime Minister, and a partial solar eclipse.