In her first speech in the role, she acknowledged the economic headwinds facing the country but promised action this week to help with energy bills.
Speaking in Downing Street, she said: “I’m confident that together we can ride out the storm, we can rebuild our economy and we can become the modern brilliant Britain that I know we can be.
“This is our vital mission to ensure opportunity and prosperity for all people and future generations. I’m determined to deliver.”
Ms Truss became Prime Minister in Balmoral after an audience with the Queen, who had earlier received Boris Johnson’s resignation.
While Mr Johnson had delivered his farewell speech in sunshine, Ms Truss had to dodge torrential showers in Westminster for her address from a podium outside the black door of No 10.
She vowed to create an “aspiration nation”, promising to tackle the issues that have been holding Britain back for years by building “roads, homes and broadband faster”.
In an echo of Winston Churchill, she promised “action this day” to deliver her plans to transform the country.
But in an acknowledgement of the immediate problem facing households across the country, she said: “I will take action this week to deal with energy bills and to secure our future energy supply.”
A Government source confirmed a report in The Times that the energy freeze will be around the £2,500 mark, although an insider in the Truss camp said “nothing is finalised yet”.
The plan is based on the current £1,971 energy price cap plus the £400 universal handout announced under Mr Johnson’s government.
Help is also expected for business customers struggling with soaring bills which are not covered by the existing energy price cap in England, Scotland and Wales.
As well as dealing with the energy crisis, Ms Truss said her early priorities included “a bold plan to grow the economy through tax cuts and reform” and “get Britain working again”.
Boris Johnson delivered Brexit, the Covid vaccine and stood up to Russian aggression. History will see him as a hugely consequential prime minister
Liz Truss on her predecessor
She also promised to “put our health service on a firm footing” so “people can get doctor’s appointments and the NHS services they need”.
After the downpour which preceded her speech, Ms Truss said: “We shouldn’t be daunted by the challenges we face.
“As strong as the storm may be, I know that the British people are stronger.
“Our country was built by people who get things done. We have huge reserves of talent, of energy and determination”.
Shortly after finishing her speech in Downing Street, Ms Truss headed to Parliament where she began a cull of ministers who had been loyal to her leadership rival Rishi Sunak.
Among the casualties were deputy prime minister and justice secretary Dominic Raab, transport secretary Grant Shapps and health secretary Steve Barclay.
Ms Truss then rewarded allies, with Kwasi Kwarteng taking the key post of Chancellor, Therese Coffey becoming Deputy Prime Minister and Health Secretary, while James Cleverly has been appointed Foreign Secretary.
But Nadine Dorries turned down the offer to stay on as culture secretary, while former Tory leader Sir Iain Duncan Smith said that he had also rejected a Cabinet post.
In her speech outside No 10, Ms Truss paid tribute to her predecessor, saying that “Boris Johnson delivered Brexit, the Covid vaccine and stood up to Russian aggression”.
“History will see him as a hugely consequential prime minister.”
In his own address before leaving Downing Street for the final time as prime minister, Mr Johnson called for the Tory party to unite behind his successor, but he could not conceal his bitterness at the way he was ousted.
He suggested he would now slip into political obscurity, although a reference to Roman statesman Cincinnatus fuelled speculation he could consider a comeback.
Mr Johnson said “I will be offering this government nothing but my most fervent support”, calling for Tories to back the new leader at a “tough time for the economy”.
Watched by wife Carrie Johnson, he added that if the couple’s dog Dilyn and Larry the No 10 cat can “put behind them their occasional difficulties”, then “so can the Conservative Party”.
But in a sign of lingering resentment at the manner in which he was forced out, Mr Johnson said that “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”.
He said his career was now like a booster rocket “that has fulfilled its function and I will now be gently re-entering the atmosphere and splashing down invisibly in some remote and obscure corner of the Pacific”.
Mr Johnson declared “like Cincinnatus, I am 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” like the Roman statement who heeded the call to serve his people.
Congratulations to Prime Minister Liz Truss.
I look forward to deepening the special relationship between our countries and working in close cooperation on global challenges, including continued support for Ukraine as it defends itself against Russian aggression.
— President Biden (@POTUS) September 6, 2022
US President Joe Biden offered his congratulations to the new Prime Minister, saying he looked forward to “deepening the special relationship between our countries and working in close cooperation on global challenges, including continued support for Ukraine as it defends itself against Russian aggression”.
But the transatlantic relationship could be strained if Ms Truss pushes ahead with the plan to override parts of Northern Ireland’s Brexit deal – Mr Biden is proud of his Irish roots and takes a keen interest in the issue.