Steve Barclay has been appointed as health secretary, Downing Street has announced.
Mr Barclay was previously the chancellor of the Duchy of Lancaster and chief of staff for Downing Street.
It comes after Sajid Javid's shock resignation, which was followed by Chancellor Rishi Sunak.
The two senior cabinet ministers spectacularly quit earlier on Tuesday evening as Boris Johnson battled to remain in Number 10 amid growing questions over his handling of the row over disgraced deputy chief whip Chris Pincher's conduct.
Mr Pincher quit as deputy chief whip last week following claims that he groped two men at the upmarket Carlton Club, but Mr Johnson knew about allegations against him as far back as 2019.
The prime minister acknowledged he should have sacked Mr Pincher when he was found to have behaved inappropriately when he was a Foreign Office minister in 2019, but instead went on to appoint him to other government roles.
But the apology from the PM for appointing Mr Pincher to the role was unable to prevent the two former cabinet ministers' departures which occurred within minutes of each other.
Mr Javid said the British people "expect integrity from their government" but voters now believed Mr Johnson's administration was neither competent nor "acting in the national interest".
Responding to Mr Javid's resignation, the PM told the former health secretary he was "sorry" to receive his letter as and suggested his government would "continue to deliver" plans for the NHS.
In a brief letter, the prime minister said: "Dear Saj, Thank you for your letter this evening tendering your resignation. I was very sorry to receive it.
"You have served this government, and the people of the United Kingdom, with distinction."
He concluded: "You will be greatly missed, and I look forward to your contribution from the backbenches."
The twin resignations of Mr Javid and Mr Sunak mean Mr Johnson's position remains perilous, but cabinet ministers including Dominic Raab, Liz Truss, Michael Gove, Therese Coffey and Ben Wallace indicated they would be staying in the government and still support the PM.
The loss of crunch by-elections in Tiverton and Honiton and Wakefield in June triggered the resignation of party chairman Oliver Dowden last month.
The position of Conservative Party chairman remains unfilled, as do the roles of chancellor and vice party chairman, following the departures of Mr Javid and Bim Afolami who resigned live of television on Tuesday evening.
The PM is also now recruiting the fourth Downing Street chief of staff of his tenure after appointed Mr Barclay to health secretary.
The prime minister's fate may ultimately lie with backbench MPs if the Tory 1922 Committee's rules are changed to allow another confidence vote within 12 months.
The PM narrowly survived a confidence vote last month but suffered a rebellion bigger than Theresa May.
Some 211 MPs voted for the prime minister, compared to 148 votes against - a majority of 63.
He needed a simple majority - 180 votes or more - to continue in office.
The result meant 59% of Conservative MPs backed Mr Johnson, with 41% voting against him.