Matt Hancock has resigned as Health Secretary after he breached social distancing guidance by kissing a colleague.
In a letter to the PM he said the government “owe it to people who have sacrificed so much in this pandemic to be honest when we have let them down”.
Boris Johnson said he was “sorry” to receive the resignation.
Former chancellor Sajid Javid has said he is “honoured” to have been chosen as Mr Hancock’s replacement.
Hancock had been under increasing pressure to quit, after the Sun published pictures, and then a video of Hancock and Gina Coladangelo, who are both married with three children, kissing.
The newspaper said they had been taken inside the Department of Health on 6 May.
Hancock has ended his 15-year marriage to his wife, Martha, and the relationship with Ms Coladangelo is understood to be a serious one.
Fellow Tory MPs, as well as Labour and the COVID-19 Bereaved Families for Justice group, had called for the health secretary to be sacked and a senior Tory figure told the BBC that many MPs had told their whips on Saturday that he ought to resign.
BBC political editor Laura Kuenssberg said No10 had stressed that it had been Hancock’s decision to go and that he had not been pushed out by the prime minister.
She said Ms Coladangelo was also leaving her role as a non-executive director of the Department of Health.
In a video posted on Twitter, Mr Hancock said: “I have been to see the prime minister to resign as secretary of state for health and social care.
“I understand the enormous sacrifices that everybody in this country has made, that you have made, and those of us who make these rules have got to stick by them and that’s why I have got to resign.”
In his resignation letter, Mr Hancock, who served as health secretary for three years, reiterated his apology for “breaking the guidance” and he apologised to his family and loved ones for “putting them through this”.
In response, the prime minister said Hancock “should leave office very proud of what you have achieved – not just in tackling the pandemic, but even before COVID-19 struck us”.
He added: “I am grateful for your support and believe that your contribution to public service is far from over.”
Javid, who has held several key roles in government, said he was “honoured” to be appointed as health secretary “at this critical time”.