Green, 61, stepped down after a parliamentary investigation found he had breached the ministerial code of conduct by making "inaccurate and misleading" statements about what he knew about claims that pornography had been found on a computer in his House of Commons office in 2008.
"I apologise that my statements were misleading on this point," he said in his resignation letter.
Green, who had been under investigation regarding allegations of inappropriate conduct, had previously denied suggestions that he made unwanted advances to a female journalist, Kate Maltby, in 2015 and viewed pornography on a computer in his Commons office in 2008.
An official report by the UK Cabinet Office found that statements he had made about being unaware pornographic material had been found on his computer were "inaccurate and misleading" and as such fell short of the ministerial code.
The report also found that although there were "competing and contradictory accounts of what were private meetings" between himself and Ms Maltby, "the investigation found Ms Maltby's account to be plausible".