Mr Trump and his wife Melania Trump will meet the monarch at the castle next Friday.
The President has not been honoured with a state visit, the trappings of which include an official banquet at Buckingham Palace or a carriage procession up the Mall.
Mr Trump will then rejoin Melania, who is being hosted by Mrs May’s husband Philip on a separate schedule that morning, for their visit to meet the Queen at Windsor.
Instead the president will be whisked off for a tour of some of England’s most impressive historic buildings before departing for Scotland for a relaxing weekend, part of which is expected to be spent on the golf course.
The visit takes in a lavish black-tie dinner at Blenheim Palace, a working lunch with Theresa May at her country residence Chequers and a meeting with the Queen at Windsor Castle, but only a brief overnight stay in London.
It seems unlikely that the President will come close enough to Westminster to see a “Trump baby” blimp which protesters plan to fly over the Houses of Parliament, after receiving permission for the stunt from London Mayor Sadiq Khan.
Asked whether the President’s schedule was designed to keep him away from possible protests, a Downing Street spokeswoman said: “Prime ministers frequently make use of Chequers for meetings with foreign leaders. It offers a more informal setting for important bilateral discussions.”
Previous presidents Richard Nixon, George Bush Senior and George Bush Junior have all visited the 16th-century country Buckinghamshire manor house for meetings with former PMs.
“We’re looking forward to making sure the president has a chance to see and experience the UK beyond London and the South-East,” said the Number 10 spokeswoman.
She added: “As with any protest, we are a free and open democracy and we believe in the right to peaceful protest. But I would also say that I think the majority of British people understand the importance of the UK-US alliance.
“The presidential visit is an important moment to recognise our close and special relationship and to have good and frank discussions on the key issues.”
Mr Trump arrives in the UK on board Air Force One next Thursday afternoon, straight from the Nato summit in Brussels where he is expected to confront European allies over levels of defence spending.
The president and his wife Melania will then be guests of honour at a dinner for around 100 guests in the spectacular setting of Blenheim Palace in Oxfordshire.
The monumental 18th-century country house, built for the first Duke of Marlborough as a reward for his military victories, was the birthplace of Sir Winston Churchill, a personal hero of the president.
The event will begin with a military ceremony in the Great Court of the Palace, where the bands of the Scots, Irish and Welsh Guards will play the Liberty Fanfare, Amazing Grace, and the National Emblem.
Hosted by the Prime Minister, guests at the dinner will include leaders of UK business sectors including financial services, travel, creative industries, food and drink, engineering, tech, infrastructure, pharmaceuticals and defence.
Downing Street said the dinner was intended to “celebrate the strong business links between our two countries” at a time when the UK is hoping to strike a free trade deal with the US following Brexit.
During dinner, the Countess of Wessex’s Orchestra will perform a series of classic British and American music hits. And on his departure, Mr Trump will be “piped out” by the Royal Regiment of Scotland.
The President and his wife will spend Friday night at the US Ambassador’s London residence Winfield House, in Regent’s Park.
The 1930s mansion is set within a large garden – second only to Buckingham Palace in the capital – with tight security to keep any protesters at bay.
The president and first lady will fly on Friday evening to Scotland. Further details on their schedule north of the border are not yet available, but it is understood that there will be limited Government involvement in what was being described as a private element of the official visit.