Damian Green has been sacked from the cabinet amid allegations that pornographic material was found on a Commons computer in 2008.
Mr Green was asked to resign as First Secretary of State for breaches of the ministerial code.
It came after an investigation by the Cabinet Office found suggestions he was not aware indecent material was found, were "inaccurate and misleading".
On Friday, the morning after his sacking, Mr Green faced the media outside his home but declined to answer questions, insisting: "I'm not going to say anything beyond my statement."
In his letter to the prime minister Mr Green apologised and spoke of his "regret" at being asked to resign.
Mrs May said she was "extremely sad" to ask her close ally to resign but stressed his behaviour "falls short" of the Seven Principles of Public Life.
The prime minister's de facto deputy had strongly denied claims that pornographic material was found on one of his parliamentary computers.
In his letter to Mrs May, Mr Green wrote: "From the outset I have been clear that I did not download or view pornography on my Parliamentary computers.
I accept that I should have been clear in my press statements that police lawyers talked to my lawyers in 2008 about the pornography on the computers, and that the police raised it with me in a subsequent phone call in 2013. I apologise that my statements were misleading on this point.
"The unfounded and deeply hurtful allegations that were being levelled at me were distressing both to me and my family and it is right that these are being investigated by the Metropolitan Police's professional standards department."
In her letter to Mr Green, the prime minister said: "While I can understand the considerable distress caused to you by some of the allegations which have been made in recent weeks, I know that you share my commitment to maintaining the high standards which the public demands of ministers of the Crown.
"It is therefore with deep regret, and enduring gratitude for the contribution you have made over many years, that I asked you to resign from the Government and have accepted your resignation."
The alleged pornographic material found was deemed lawful but one of the investigating officers said some of it was "extreme".
Mr Green had been the subject of an inquiry after journalist Kate Maltby alleged that he made inappropriate advances to her, claims he strenuously denies.
Mr Green apologised to Ms Maltby in his letter, but maintained he did "not recognise the events" she described.
"I deeply regret the distress caused to Kate Maltby following her article about me and the reaction to it," he said.
The inquiry was triggered after Ms Maltby claimed Mr Green "fleetingly" touched her knee during a meeting in a pub in 2015, and a year later sent her a "suggestive" text message after she was pictured wearing a corset in a newspaper.
Cabinet Secretary Sir Jeremy Heywood said that with "competing and contradictory accounts of what were private meetings" it was "not possible to reach a definitive conclusion on the appropriateness of Mr Green's behaviour with Kate Maltby in early 2015, though the investigation found Ms Maltby's account to be plausible".
Labour MP Jess Phillips, who had earlier said Mr Green should lose his job over the porn allegations told ITV News on Wednesday, said his sacking was a "tiny signal that things are going in one direction".
"It has never been about the scalp. It has always been about changing this culture," she said.
"I don't want people losing their jobs left right and centre, I want this place to show demonstrably that it can change and that this sort of behaviour whether it's sexual harassment or inappropriate behaviour at work just won't be tolerated anymore," she said.
Stella Creasy said: "Above all else what we're all looking for is the cultural change and the systems in place to make sure that if anybody does come forward they're investigated independently of any political party involvement and that then it's done quickly and fairly to both sides and that then there are consequences to it. I'm not sure we can say we're there yet."
A source close to Brexit Secretary David Davis confirmed he would not quit the Government in protest at Mr Green's sacking, despite a report earlier this month that he had threatened to resign if the First Secretary of State was forced out over the material found by the police.