The resignation of one of May's most trusted allies, who had helped pacify her deeply divided party, is a blow as she navigates the final year of tortuous negotiations towards Britain's exit from the European Union in March 2019.
Green, who voted to stay in the EU, was appointed as first secretary of state just six months ago in a bid to shore up May's premiership following her disastrous bet on a June snap election that lost her party its majority in parliament.
But Green's future was thrust into doubt when the Sunday Times newspaper reported last month that police in 2008 had found pornography on his office computers in the Houses of Parliament. In response, Green said the story was untrue.
A review, requested by May and conducted by a senior government official, concluded that Green's statements which suggested he was not aware that indecent material had been found on the computers, were "inaccurate and misleading."
The inquiry, a summary of which was distributed by May's Downing Street office, found he had breached rules governing the behaviour of ministers.
"I regret that I've been asked to resign from the government following breaches of the Ministerial Code, for which I apologise," Green said in a letter to May, who said she had accepted his resignation with deep regret.
Green, 61, said he did not download or view pornography on his parliamentary computers. He added that he should have been clearer about his statements after the story broke.
He is the most senior British politician to fall since a debate about a culture of abuse by some powerful men at the heart of Westminster was triggered by the Harvey Weinstein sexual harassment scandal.
May's defence minister, Michael Fallon, quit last month for unspecified conduct which he said had fallen below required standards. Her aid minister resigned a week later after holding undisclosed meetings with Israeli officials.
Conduit For Complaints
During the turmoil that followed the botched election, May turned to Green - a friend and ally from their days at Oxford University - to stabilise her premiership and appease those within the Conservative Party who wanted her to quit.
One of his key roles was to act as a conduit for disgruntled party members who felt they had been ignored in May's election campaign. He sought to help her to shed the image of a distant leader who only listens to those in her inner circle.
"It's another blow for May but it is not deadly in any way at all," said Anand Menon, professor of European politics at King's College London. "She has lost her soulmate in cabinet but this is not the end of Prime Minister May."
The internal investigation found that Green's conduct as a minister was generally "professional and proper" but found two statements he made on Nov. 4 and 11 to be inaccurate and misleading.
In the statements he had suggested he was not aware that indecent material was found on parliamentary computers in his office.
"These statements ... constitute breaches of the Ministerial Code. Mr Green accepts this," the report summary said.
Sexual abuse allegations against Hollywood producer Weinstein have prompted some women and men to share stories about improper behaviour at the heart of British political power in Westminster.
"Everyone who wants to play their part in our political life should feel able to do so - without fear or harassment, and knowing they can speak out if they need to," May said in her letter to Green.
The internal investigation also addressed allegations, made by the daughter of a family friend, that Green had made an unwanted advance towards her during a social meeting in 2015, had suggested that this might further her career, and later had sent her an inappropriate text message.
The report said it was not possible to reach a definitive conclusion on the appropriateness of Green's behaviour in that instance, though the investigation found allegations to be plausible.
Green said in his resignation letter that he did not recognise the account of events, but apologised to the woman, academic and critic Kate Maltby, for making her feel uncomfortable.
(Writing by Guy Faulconbridge; editing by Susan Thomas and John Stonestreet)
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)