The Queen will receive the new prime minister at her Balmoral estate in Scotland for the first time in her long reign.
Her Majesty will meet them on 6 September, a day after the new prime minister is announced.
She would normally appoint prime ministers from Buckingham Palace or Windsor Castle.
However, the 96-year-old monarch has been advised to remain at her Balmoral residence in Aberdeenshire, where she is enjoying her summer holiday.
It will be from there that she will install either Rishi Sunak or Liz Truss as prime minister on 6 September, breaking years of royal precedent.
On Wednesday, a Buckingham Palace spokesperson said: “The Queen will receive Prime Minister Boris Johnson on Tuesday September 6 at Balmoral, followed by an audience with the new PM.”
It is understood the decision was taken at this stage in order to provide certainty for the prime minister’s diary.
If the Queen had experienced an episodic mobility issue next week and the plan had been to travel to London or Windsor, it would have led to alternative arrangements at the last minute.
Since last autumn, the Queen has suffered with mobility issues and now regularly uses a walking stick.
This year, she has been forced to cut several official engagements short, and she notably missed much of her Platinum Jubilee celebrations, only appearing briefly on the palace balcony.
In June, she missed Royal Ascot for the first time since her coronation, with the Duke of Kent taking her place in leading the royal carriage procession.
She also contracted COVID-19 back in February, and later spoke about how it left her feeling “very tired and exhausted”.
The winner of the Tory leadership contest to succeed Boris Johnson is set to be announced on Monday 5 September.
His successor will then travel to Balmoral to be officially appointed by the Queen the following day.