Rishi Sunak says he is not "not daunted" and understands he will have to work to restore trust, after becoming the UK's third prime minister in three months.
The former chancellor has officially become UK prime minister after meeting King Charles at Buckingham Palace on Tuesday.
Speaking outside Number 10 Downing Street, he promised he would earn people's trust, adding he understood there would be work to do "after all that has happened".
"I know the high office that I have accepted and I hope to live up to its demands but when the opportunity to serve comes along, you cannot question the moment, only the willingness.
"I stand here before you, ready to lead our country into the future, to put your needs above politics, to reach out and build a government that represents the very best traditions of my party.
"Together we can achieve incredible things. We will create a future worthy of the sacrifices so many have made and fill tomorrow and every day thereafter with hope," he said.
He paid tribute to his predecessor Liz Truss, but added "some mistakes were made".
He said they were "not born of ill will or bad intentions. Quite the opposite, in fact. But mistakes nonetheless".
He said the work to fix these would begin "immediately".
Mr Sunak also hailed Boris Johnson's "incredible achievements" as prime minister.
Mr Johnson said all Conservatives should give Mr Sunak their "wholehearted support".
Labour leader Keir Starmer congratulated Mr Sunak on being the country's first Asian prime minister, but said the public needed a "fresh start and a say in Britain's future".
Mr Sunak has previously ruled out an early general election.
General elections are held every five years in the UK, and the next is not due until January 2025.
Earlier on Tuesday local time Liz Truss used her final speech as British prime minister to claim "brighter days are ahead".
The UK's shortest-serving prime minister said in "just a short period" her government had acted "urgently and decisively" and helped thousands of businesses avoid bankruptcy.
Ms Truss said she "believed in Britain", before wishing her successor "every success".
"Our country continues to battle through a storm. But I believe in Britain. I believe in the British people. And I know that brighter days lie ahead."
She used her final farewell to champion the low-tax ideology she attempted to pursue in office, and urged the country to take hold of its "Brexit freedoms".
"From my time as prime minister, I am more convinced than ever, that we need to be bold and confront the challenges that we face," she said, before invoking Roman philosopher Seneca.
Mr Sunak was the only candidate for the Conservative Party leadership, after Mr Johnson, and then House of Commons leader Penny Mordaunt bowed out of the race.
The millionaire and former hedge fund boss is the first British prime minister of Indian heritage, and at 42, the youngest in more than 200 years.
Last week, Mr Hunt rolled back nearly all the tax cut measures in Ms Truss's disastrous mini-budget.
Ms Truss was forced to resign earlier this month after 45 chaotic days in power — the shortest tenure of any British prime minister.
Cabinet shuffled as Braverman returns
Mr Sunak immediately set about filling the posts in his government, aiming to put his stamp on the government while bringing in people from different wings of the Conservative Party.
He removed about a dozen members of Ms Truss’s cabinet, but kept several senior figures in place, including Foreign Secretary James Cleverly, Defence Secretary Ben Wallace and Chancellor of the Exchequer Jeremy Hunt.
Penny Mordaunt, who ended her bid to win a leadership contest against Mr Sunak on Monday, also retained her position as leader of the House of Commons, a role that organises the government's business in the lower house of parliament.
Home Secretary Suella Braverman, who resigned after breaching the ministerial code, a move that helped trigger Ms Truss's downfall, got her previous job back.
Mr Sunak also brought back faces from the ear of Ms Truss's predecessor, Boris Johnson, including Deputy Prime Minister Dominic Raab.
Kemi Badenoch, who earlier this year was a contender in a Conservative Party leadership contest to replace Mr Johnson, was re-appointed as Trade Minister and also given the role of Equalities Minister.
Michael Gove has been appointed as the country's Levelling-up Minister, a role responsible for plans to close the gap between rich and poor parts of the country.
With his new appointments, Mr Sunak was seen to be drawing ministers from across the Conservative Party while leaving others in post — a move that should ease concerns that Mr Sunak might appoint loyalists rather than try to unify the party.
ABC/Wires
