Penny Mordaunt had until 2pm on Monday (midnight AEDT) to have the declared support of at least 100 Tory MPs, a threshold Sunak had already cleared.
Mordaunt publicly conceded just minutes before the deadline, offering Sunak her full support and urging her colleagues to unite behind Sunak.
Shortly after, Graham Brady, the head of the powerful 1922 Committee that controls Tory leadership contests, confirmed Sunak was the only MP to achieve the necessary support and had been elected leader of the Conservative Party.
As leader of the ruling party, Sunak will replace Truss as prime minister, becoming Britain’s first leader of colour.
Mordaunt’s camp had spent Monday morning scrambling to gather the required number of supporters to force a vote of the party’s members, despite Sunak having a commanding lead among MPs who had publicly declared their position.
In pulling out of the race, Mordaunt, who is the leader of the House of Commons, said it was clear her colleagues felt “certainty” was needed.
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“This decision is an historic one and shows, once again, the diversity and talent of our party,” she said, in a statement.
“Rishi has my full support, I am proud of the campaign we ran and grateful to all those, across all sides of our party, who gave me their backing.
“We all owe it to the country, to each other and to Rishi to unite and work together for the good of the nation.”
The opposition Labour Party has been loudly calling for a general election in recent days, following weeks of chaos under Truss who became prime minister after Boris Johnson was forced to quit after losing support of his party over multiple scandals.
Sunak is expected to address Tory MPs at 2.30pm on Monday (12.30am Tuesday AEDT).