Green, 61, has been a close friend of May since they were at Oxford University, and he is one of her closest political allies.
Green was appointed in the wake of her disastrous bet on a June snap election which lost her party its majority in parliament.
He was under investigation over claims pornography was found on his computer in 2008 and that he had acted inappropriately towards journalist Kate Maltby.
"I have also carefully considered the report's conclusions in relation to two statements you made on 4 and 11 November which you now accept were inaccurate and misleading", the prime minister wrote in a letter requesting Green to step aside.
However Mr Green told the public and MPs he hadn't been informed by police that pornography had been found.
Drama Plays Out In One Race Of Virginia House Of Delegates
Virginia Board of Elections Chairman James Alcorn said the board will likely pick the victor the same way it picks ballot order. The official wrote that although he signed off on the ballot, which was not counted a day earlier, he was confused at the time.
"I do not recognise the events she described in her article, but I clearly made her feel uncomfortable and for this I apologise", he wrote.
'It is therefore with deep regret and enduring attitude for the contribution you have make over many years, that I asked you to resign from the Government and have accepted your resignation'.
He left his cabinet post after an investigation found he breached United Kingdom ministerial code by misleading the public about whether he knew porn had been found on his computer. He reiterated his claim that he did not download or view any pornography on his office computer.
Mrs May added: '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 highs standards which the public demand of minsters of the crown. "Mr Green accepts this".
The computer was one of a number of possessions seized by the police during a controversial inquiry into the leaking of official documents by a civil servant to Mr Green, at the time a shadow Home Office minister under David Cameron and his immediate boss, then shadow home secretary David Davis.
Child Health Insurance Program running out of money
A federal program that helps families without medical insurance get it for their kids is running out of money. Affected households are slated to receive notifications about the decision via mail.
Ms Maltby is not commenting on Mr Green's resignation until she receives more details from the Cabinet Office.
Theresa May told him in a letter than she had asked him to resign, and accepted his resignation.
His sacking could pile more pressure on the PM following the resignations in recent weeks of Sir Michael, and Priti Patel as global development secretary over undisclosed meetings in Israel.
She had fought for weeks to try and find a way to save him, but eventually decided he must go.
Pa. moves past IL to No. 5 in population
The state's population now stands at almost 28.3 million residents -an increase of more than 3 million residents since 2010. Rogers says Utah landed at No. 3 on the list at 1.9 percent due to more births than deaths in that state.