Ms Truss met with the monarch in the drawing room of Balmoral Castle, where she was invited to form a government.
She arrived in Aberdeenshire, around 40 minutes after former Prime Minister Boris Johnson resigned in a private audience with Her Majesty.
Ms Truss swept onto the Queen’s private Scottish estate in a chauffeur-driven car with her husband Hugh O’Leary.
Like her predecessor, she was welcomed by the Queen’s private Secretary Sir Edward Young and her Equerry Lieutenant Colonel Tom White.
The new Prime Minister can be seen curtseying to the monarch, as is tradition.
Liz Truss with the Queen
Jane Barlow
The Queen met with the new Tory leader at Balmoral Castle
Jane Barlow
On Tuesday morning, Mr Johnson made his final speech as Prime Minister outside No.10.
He said: “This is it, folks. Thank you everybody for coming out so early this morning. In only a couple of hours I will be in Balmoral to see Her Majesty the Queen and the torch will finally be passed to a new Conservative leader.
“The baton will be handed over in what has unexpectedly turned out to be a relay race. They changed the rules halfway through, but never mind that now.”
Ms Truss' next task will return to Westminster where she is expected to address the nation before getting down to the business of appointing her ministerial team.
A number of key allies and supporters have already been pencilled in for some of the most senior roles, including Business Secretary Kwasi Kwarteng who is widely expected to be given the crucial role of Chancellor.
If confirmed he will have the task of delivering on her promised “bold” plan to deal with surging energy bills which have plunged households and businesses into crisis.
Details could be set out as early as Thursday as the new administration seeks to reassure worried voters following a summer of political paralysis.
Other key appointments are expected to include Attorney General Suella Braverman, who is tipped for promotion to Home Secretary, and Education Secretary James Cleverly, who is expected to be the new Foreign Secretary.
Therese Coffey, the Work and Pensions Secretary who is described as Ms Truss’s closest friend at Westminster, is thought to be in line to become Health Secretary while Ben Wallace is expected to remain as Defence Secretary.
Other appointments will be closely scrutinised by Tory MPs for signs that she is prepared to bring in ministers who did not necessarily support her in the leadership race.
Ms Truss did not enjoy the support of the majority of MPs during the parliamentary stage of the contest, with former chancellor Mr Sunak coming out on top among fellow Tories.
And her 57 percent to 43 percent margin of victory in the final ballot of the party, while comfortable, was still narrower than the last three Tory leadership contests that went to a vote.