The former chancellor – who quit on Tuesday helping to trigger an avalanche of ministerial resignations – announced his decision on Twitter saying: “Let’s restore trust, rebuild the economy and reunite the country.”
His move came as allies of former foreign secretary Jeremy Hunt – who was runner-up to Mr Johnson in 2019 – said he was “virtually certain” to stand again this time.
Meanwhile, Mr Johnson was continuing to resist demands to stand down as Prime Minister and hand over to his deputy, Dominic Raab, until a permanent successor is in place.
In a glossy launch video in which he set out his family history, Mr Sunak said: “Our country faces huge challenges, the most serious for a generation.
“And the decisions we make today will decide whether the next generation of British people will also have the chance of a better future.”