Mr Sunak was the only Tory leadership candidate to get the backing of at least 100 Conservative MPs, meaning he will become leader without the party’s members having a vote.
The former Chancellor was initially opposed by Boris Johnson, who backed out of the leadership race over the weekend despite claiming to have received sufficient support from MPs to continue, and Penny Mordaunt, who was unable to gather the 100 backers needed to proceed in the contest.
Unlike Mordaunt, Mr Sunak swiftly hit the threshold of 100 nominations from Conservative colleagues ahead of the deadline of 2pm on Monday before commanding the public support of about half the parliamentary party.
Rishi Sunak in profile
Sunak will become Prime Minister just seven weeks after losing out to Liz Truss in the last Tory leadership contest.
Ms Truss resigned after just 44 days in office last week.
Announcing her resignation, the prime minister said: “I recognise I cannot deliver the mandate on which I was elected by the Conservative Party.
“I am resigning as leader of the Conservative Party. There will be a leadership election to be completed within the next week.
“I will remain as prime minister until a successor has been chosen.”
Victory for Mr Sunak means the Tories are on to their third prime minister since they won the 2019 general election under Mr Johnson’s leadership.
Veteran Tory Sir Christopher Hope joined Labour in demanding a fresh general election, arguing it is the only solution for the next leader now the Conservative Party is “ungovernable”.
The MP for Christchurch in Dorset, which he held last time with a near-25,000 vote majority, told Today: “The best way they can get that respect is by winning a mandate with the people, and that’s why I think a general election is essentially the only answer, otherwise we’re just going to go from bad to worse.
“The party is ungovernable in the House of Commons and so we’re going to have continuing rebellions as we try to change policies and so on, and so I must say I’m very pessimistic, I’m very angry, and I feel that Boris has been let down once again and undermined by our parliamentary colleagues.”