A photo from inside the drawing room at Balmoral showed the Queen smiling as she shook Ms Truss's hand while she held an audience with the incoming PM.
The 96-year-old monarch, wearing a grey cardigan and pleated tartan skirt, clutched a walking stick as she invited her new prime minister to form a government.
In a statement, Buckingham Palace said: “The Queen received in audience The Right Honourable Elizabeth Truss MP today and requested her to form a new administration. Ms Truss accepted Her Majesty’s offer and kissed hands upon her appointment as Prime Minister and First Lord of the Treasury.”
Ms Truss is the 15th PM the Queen has sworn in during her 70-year reign.
She arrived shortly after Boris Johnson left the royal residence with wife Carrie after handing in his resignation to the monarch, which she was "graciously pleased to accept", said Buckingham Palace.
Earlier, in his final speech as prime minister, Mr Johnson hinted he could make a comeback to frontline politics.
He compared himself to an Ancient Roman leader who, according to legend, returned from retirement to serve once more at a time of crisis.
Ms Truss and husband Hugh O'Leary were waved goodbye by the Queen’s private Secretary Sir Edward Young and her Equerry Lieutenant Colonel Tom White as they left the Scottish residence.
Matters discussed during Liz Truss's audience at Balmoral is a conversation that will remain solely between the Queen and her new prime minister, as Royal Editor Chris Ship explains
The former foreign secretary is now heading back to London, where she will prepare to deliver her first speech as prime minister on Tuesday afternoon.
Facing one of the most challenging in-trays of any British peacetime leader, Ms Truss will start working on an emergency support package to deal with the escalating energy crisis.
She is expected to briefly outline her vision for tackling the soaring cost of living and reassure the nation that help will be on the way.
An announcement setting out the details of the plan is expected this week, but she is reportedly drawing up plans for a freeze in bills which could cost around £100 billion.
Following Ms Truss's speech on Tuesday, she will then disappear behind the doors of No 10 to begin appointing her Cabinet.
ITV News understands she has already chosen many of the top roles, with Kwasi Kwarteng tipped for the crucial job of chancellor who will be tasked with delivering on her "bold" plan to deal with skyrocketing energy bills.
Her Cabinet will also focus heavily on growing the economy and dealing with the NHS's record backlog - something close friend Therese Coffey is expected to be put in charge of as health secretary.
Ms Truss will face her first session of Prime Minister’s Questions in the Commons on Wednesday.
After meeting with the Queen earlier on Tuesday, Ms Truss's team swiftly updated her Twitter profile to reflect her new role to read: "Prime Minister of the United Kingdom of Great Britain and Northern Ireland. Leader of the Conservative Party. MP for South West Norfolk."
Earlier, former PM Mr Johnson and wife Carrie spent almost 40 minutes with Her Majesty in the drawing room of the private royal residence, as his three-year premiership came to a close.
Boris and Carrie Johnson arriving at Balmoral Castle earlier on Tuesday
In a statement, Buckingham Palace said: “The Right Honourable Boris Johnson MP had an audience of The Queen this morning and tendered his resignation as Prime Minister and First Lord of the Treasury, which Her Majesty was graciously pleased to accept.”
Following his departure from Balmoral, Mr Johnson also quickly updated his Twitter bio to reflect his new status as "former Prime Minister of the United Kingdom".
During his farewell speech, the former PM described the transferring of power to his successor as "handing over the baton" as he lamented his premiership had "unexpectedly turned out to be a relay race".
In what appeared to be a swipe at the many who resigned from his government and ultimately triggered his downfall, he suggested he was forced out of power after "they changed the rules halfway through - but never mind that now".
But he told Conservatives that "it's time for politics to be over, folks" as he urged the party to unite behind Ms Truss. Mr Johnson said: “I know that Liz Truss and this compassionate Conservative government will do everything we can to get people through this crisis and this country will endure it and we will win.”
Senior Tory Sir Bernard Jenkin urged Ms Truss to “level with the British people” about the “utterly dire situation” the country faces in her first speech.
“We’re looking at kind of five horses of apocalypse coming at the same time, a perfect storm of crises – not just the cost-of-living crisis, not just the energy crisis, we have state-on-state war in Europe for the first time since 1945, we have embedded inflation and the public finances are already shot to pieces," he told BBC Radio 4's World at One programme.
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He added that “she’s got to prepare people, we’re not in sunny uplands”, while warning that the freezing of energy bills “is a short-term fix” as the war in Ukraine could go on for years.
Opposition politicians again called for oil and gas firms to pay for the freeze in bills, rather than letting taxpayers pick up the tab.
Liberal Democrat leader Sir Ed Davey said: “Liz Truss spent weeks during this summer leadership contest leaving families and pensioners worried and in limbo by refusing to set out her plans to tackle soaring energy bills.
“Now she seems set to make our children pick up the tab for this mess, while letting oil and gas firms making record profits off the hook.”