Earlier, Boris Johnson formally resigned as the head of the UK government in an audience with the Queen.
Truss is the 15th Prime Minister to serve during Queen Elizabeth II's reign, the first being Winston Churchill in 1952.
Until now, the constitutional process of the monarch inviting the leader of the majority party to form a government in her name has taken place at Buckingham Palace in London. But with the Queen cutting back on her travels, it had been decided that she would receive Johnson and Truss at her summer residence of Balmoral Castle in Aberdeenshire, Scotland, marking a historic first.
After her meeting with the Queen, Truss left Balmoral Castle to return to London where she will deliver her inaugural speech as Prime Minister before she begins unveiling her top team in the Cabinet.
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Attorney General Suella Braverman is expected to be the only Indian-origin MP in her top team, as the Goan-origin former leadership contender is expected to be promoted to replace Priti Patel, who resigned as Home Secretary on Monday evening.
Rishi Sunak, the British Indian former finance minister who lost his Tory leadership bid 57-43 per cent, has almost ruled out the prospect of serving in a Truss-led Cabinet. Among the other key posts in the new Cabinet, Business Secretary Kwasi Kwarteng - a close ally - is being lined up as Chancellor of Exchequer and Education Secretary James Cleverly is to be promoted to take over Truss' current portfolio of Foreign Secretary.
Other former leadership hopefuls such as British Pakistani Sajid Javid might be offered Northern Ireland Secretary and Chancellor Nadhim Zahawi could be shifted to the role of Cabinet Office minister.
A handful of incumbent ministers, such as Defence Secretary Ben Wallace, International Trade Secretary Anne-Marie Trevelyan and Culture Secretary Nadine Dorries, are expected to retain their jobs. Therese Coffey, a close friend of Truss, is expected to replace Steve Barclay as Health Secretary.
According to UK media reports, besides the Cabinet, a widespread change of guard is also due within Downing Street with some of Johnson's senior-most aides set for an exit or reshuffle.
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