Mr Johnson will visit the 96-year-old monarch first in order to formally tender his resignation.
Afterwards, Ms Truss will have an audience - and the Queen will officially appoint her as Prime Minister.
These meetings usually take place at Buckingham Palace, and this has been the case for every one of the 14 prime ministers which Queen Elizabeth II has previously welcomed into office.
However, the Queen is currently on her summer break at Balmoral.
So, in a break from tradition, the meeting will take place in Aberdeenshire - reportedly due to concerns over the monarch’s mobility if she is forced to travel back to London.
But what exactly happens during this royal get-together, and how does the Queen appoint a new Prime Minister?
Here’s what we know about the protocol.
Why does the Queen appoint the Prime Minister?
As head of state, the appointing of new prime ministers is one of Queen Elizabeth II’s most important ‘constitutional duties’.
Other duties include the State Opening of Parliament, and signing parliamentary bills into law.
Craig Johnson, an expert in constitutional law and lecturer at Bangor University in Wales, told CNN that the Queen is still involved in the process because “it has to be remembered that the Government is still carried on in the name of the crown.”
“It is still, ‘Her Majesty’s Government,” he clarified.
Also, during the period of time between the dismissal of the former Prime Minister, and the appointment of the new one - all authority technically lies with the Queen (even if this usually lasts only for a few minutes).
What will happen during the meetings?
Although he publicly resigned on 7 July, Mr Johnson will also formally resign to the Queen during their meeting.
One of his last acts of office will be to advise Queen Elizabeth II on his successor - even if they have already been decided upon through a leadership contest.
While this moment has no real bearing on what happens, it’s a traditional quirk of the proceedings - and one which reportedly makes sure the Queen remains politically neutral.
The meeting takes place in private, and little is truly known about what happens.
Former Labour Prime Minister Gordon Brown however did touch upon the occasion in his memoir, saying it was simply a matter of “saying goodbye to the Queen - and thanking her.”
Mr Johnson’s allies have said the meeting will likely be a “very sad occasion for him.”
Shortly after, the Queen will meet with Ms Truss for a ceremonial audience known as “kissing hands”. (People often debate over whether the term is literal or not.)
Queen Elizabeth II will then invite the Tory leadership race winner to form a government - an invitation which Ms Truss will accept.
Then, there is usually a brief exchange - before the new Prime Minister shakes hands with the monarch, either bows or curtsies, and then is escorted out of the room.
When does the meeting take place?
Usually, the outgoing Prime Minister will head off to Buckingham Palace shortly after their final address outside of 10 Downing Street.
The Queen will meet with the former and new prime ministers in quick succession, and the new Prime Minister will then make their first speech to the country - also outside of Number 10.
The turnaround usually takes less than an hour, but today the timetable is slightly different.
7.30am: Boris Johnson spoke outside of Downing Street.
11.20am: Boris Johnson arrives at Balmoral Castle.
12.10pm: Liz Truss arrives at Balmoral Castle.
4pm: Liz Truss will give her first speech outside Downing Street.
What happens next?
In the coming days, Ms Truss is expected to announce her Cabinet - and lay out plans for her premiership.
Critics will be eagerly awaiting more information on the former Foreign Secretary’s plans for dealing with the spiralling cost of living crisis.
She will take part in her first session of Prime Minister’s Questions against the leader of the Labour Party, Sir Keir Starmer.