Ms Truss has taken up residence in No.10 Downing Street, after Boris Johnson formalised his resignation as PM on Tuesday.
Both Ms Truss and Mr Johnson travelled to Balmoral Castle to meet the Queen, with the new Tory leader accepting the monarch's invitation to form a government.
On Wednesday, she will face Sir Keir in the House of Commons for the first time and is expected to continue with her Cabinet reshuffle.
She held her debut meeting of her new-look Cabinet in the morning, as ministers seek to finish an emergency package to ease the cost-of-living crisis.
Liz Truss will face off with Sir Keir Starmer in PMQs on Wednesday
PA
Prime Minister Liz Truss addressing the nation outside No.10 on Tuesday
Aaron Chown
New Chancellor Kwasi Kwarteng has summoned the bosses of major banks to discuss the new economic strategy, with fresh support possibly being announced as soon as Thursday.
In her first speech as PM, Ms Truss insisted the nation can “ride out the storm” caused by Russian leader Vladimir Putin’s war in Ukraine.
Ms Truss conducted a major overhaul to leave few survivors from Boris Johnson’s Cabinet, as she failed to find a role for her leadership rival Rishi Sunak.
Her press secretary insisted the changes would “unify” the Tory party, pointing to senior roles for five leadership rivals, Penny Mordaunt, Tom Tugendhat, Suella Braverman, Kemi Badenoch and Nadhim Zahawi.
But Dominic Raab, Grant Shapps, George Eustice and Steve Barclay were among the Sunak supporters being dispatched to the backbenches.
Along with Mr Kwarteng, the appointment of Ms Braverman as Home Secretary and James Cleverly as Foreign Secretary mean that for the first time in history none of the great offices of state are held by white men.
Mr Cleverly called his appointment “an honour”, while Ms Braverman wasted little time in getting familiar with her new surroundings.
She wrote on Twitter: “Great to be at @ukhomeoffice this evening to meet the team as we begin our work: making our streets safer, supporting our security services and controlling immigration.
“Thank you to everyone at @attorneygeneral for an enjoyable 2-and-a-bit years. You are an excellent and dedicated team and achieved a huge amount of which you can be proud.”
Therese Coffey, seen as Ms Truss’s closest friend in Westminster, was appointed as Health Secretary and Deputy Prime Minister.
Jacob Rees-Mogg was appointed as Secretary of State for Business, Energy and Industrial Strategy.
Sir Keir Starmer is hoping to become Britain's next PM
Kirsty O'Connor
New Prime Minister Liz Truss and her husband Hugh O'Leary outside No.10 Downing Street
Stefan Rousseau
In his final address before leaving No 10, Mr Johnson said he would be offering the Government “nothing but my most fervent support”.
But he fuelled suspicion he could be plotting a comeback by saying like Cincinnatus, the Roman statesman, he would be “returning to my plough”.
Before entering No.10, an ambitious Mr Johnson had frequently said he would become prime minister if he was “called from my plough”.
While carrying out her reshuffle, Ms Truss made her first call to a fellow foreign leader, to President Volodymyr Zelenskyy, accepting an invitation to visit his nation soon.
She went on to speak to Joe Biden, with the White House’s account of the call making clear the US President stressed the need to come to an agreement with the EU over post-Brexit legislation on Northern Ireland.
The transatlantic relationship could be strained if Ms Truss pushes ahead with the plan to override parts of the Northern Ireland Protocol, with Mr Biden proud of his Irish roots and taking a keen interest in the issue.