Mrs May was presented with Ms Gray's report on Monday, and passed it to Alex Allan, her independent adviser on ministerial standards, who agreed with its findings.
She told Mr Green to resign on Wednesday evening, and is not expected to replace him in the immediate future.
Mr Green's demise is the result of a decade-long feud with the Metropolitan Police, whose former officers leaked details of the raid in recent weeks after the Cabinet Office originally started investigating his behaviour towards women.
Sue Gray, the Cabinet Office official who investigated Mr Green's behaviour, did not present the Prime Minister with any conclusions about whether Mr Green had behaved inappropriately towards the writer Kate Maltby, whose complaint triggered the inquiry, or whether he had ever viewed or downloaded pornography at work.
Mr Green, 61, expressed clear frustration in his resignation letter, saying: "I regret that I've been asked to resign from the Government."
His letter also contained a parting shot at the Met, saying allegations that he might have viewed pornography were "deeply hurtful" and "it is right that these are being investigated by the Metropolitan Police's professional standards department".
Mr Green accepted that police lawyers had talked to his lawyers in 2008 and that the police raised it in a subsequent phone call in 2013.
He said: "I apologise that my statements were misleading on this point." He also apologised for breaching the Ministerial Code and for making Kate Maltby, the writer who first complained about his behaviour, "feel uncomfortable".
In a letter to Mr Green, who has been a close friend since they were at university together, Mrs May said she was "extremely sad" to be writing to him, but that in the light of the report's findings his behaviour "falls short" of "the high standards which the public demands of Ministers of the Crown".
She added: "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."
However Mrs May's letter contained a stinging rebuke for the Metropolitan Police after two former officers breached a "duty of confidentiality" by revealing details of what was found on Mr Green's computer in 2008 when his parliamentary office was raided.
The Prime Minister wrote: "I shared the concerns raised from across the political spectrum when your Parliamentary office was raided in 2008 when you were a shadow home office minister holding the then Labour Government to account.
"And I share the concerns, raised once again from across the political spectrum, at the comments made by a former officer involved in that case in recent weeks. I am glad that the Commissioner of the Metropolitan Police's professional standards department are reviewing the comments which have been made."
The Cabinet Office report stated that: "Mr Green's statements of 4 and 11 November, which suggested that he was not aware that indecent material was found on parliamentary computers in his office, were inaccurate and misleading, as the Metropolitan Police Service had previously informed him of the existence of this material.
"These statements therefore fall short of the honesty requirement of the Seven Principles of Public Life and constitute breaches of the Ministerial Code. Mr Green accepts this."
The investigation concluded that because of "competing and contradictory accounts" of private meetings involving Mr Green and Ms Maltby it was not possible "to reach a definitive conclusion on the appropriateness of Mr Green's behaviour with Kate Maltby in early 2015", however, the investigation "found Ms Maltby's account to be plausible".
Miss Maltby would not comment on the news until she has received more details from the Cabinet Office.
However Miss Maltby's parents Colin and Victoria Maltby, said: "We are pleased that the Cabinet Office has concluded its enquiry into the conduct of Damian Green.
"We are not surprised to find that the inquiry found Mr Green to have been untruthful as a minister, nor that they found our daughter to be a plausible witness.
"We have received many supportive messages from people near and far who appreciate Kate's courage and the importance of speaking out about the abuse of authority.
"We join with them in admiring her fortitude and serenity throughout the length of the investigation and despite the attempted campaign in certain sections of the media to denigrate and intimidate her and other witnesses. We are proud of her.
"We have ourselves known of these incidents since they first occurred and have fully supported Kate in the responsible manner in which she has reported them."
Mr Green said in his letter: "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.
"I am grateful that the Cabinet secretary has concluded that my conduct as a minister has generally been both professional and proper. I deeply regret the distress caused to Kate Maltby following her article about me and the reaction to it.
"I do not recognise the events she described in her article, but I clearly made her feel uncomfortable and for this I apologise."
