In a statement that brought undisguised relief to Downing Street, Mr Davies said he was withdrawing his candidacy for First Minister of the new Welsh Assembly.
The MP said that he had decided to quit in the wake of "lurid and inaccurate" media reports about the incident on Clapham Common, south London, that prompted his initial resignation from the Cabinet.
The various allegations, mainly sexual, had been like "torture" because they bore no resemblance to the events that took place, he said.
Mr Davies, who will remain as MP for Caerphilly, reported to police on Monday night that he had been robbed at knifepoint on a Brixton housing estate after meeting a stranger on Clapham Common. Last night, a fifth person was arrested in connection with the incident and Mr Davies was in London to attend an identity parade.
In what he described as a "serious lapse of judgement", he had given the man a lift in his car before being robbed by another man and a woman.
In a letter to his constituency party last night, Mr Davies ended his silence on the affair with a statement that "nothing improper or illegal" had occurred, but said the incident would "haunt him for ever".
He will tell his constituency party tonight that he "will never understand why he allowed himself to get into the situation he did last Monday evening".
His decision to ditch his long-held ambition to become Wales's First Minister followed a day of intense negotiation with Downing Street, close friends and senior members of the party in Wales.
Rhodri Morgan, MP for Cardiff West - who was narrowly beaten by Mr Davies in the contest to be Labour candidate for leadership of the Welsh Assembly - announced last night that he would stand again.
A Downing Street spokesman said Mr Davies first signalled his intention to quit in a telephone call to the Prime Minister yesterday morning and confirmed his decision with a second call last night.
"The Prime Minister feels desperately sorry for Ron, who can be hugely proud of the role he has played in the Labour government since last May," the spokesman said.
"The Prime Minister sees Ron as a politician of considerable talent and has no doubt that he will continue to work with him in the future.
"He also believes Ron has impressed people with the dignified way in which he has conducted himself during the past few days."
Derek Lamb, secretary of the Caerphilly Constituency Labour Party, said: "We are all very saddened, but we understand Ron's decision entirely and we fully support him as our MP.
"Ron is being a realist. Although he was the victim of crime and had done nothing wrong there was such a furore going on around him. It really is quite unfair."
Mr Morgan, who will now emerge as one of the frontrunners to succeed Mr Davies, said he would definitely stand again. "I think Ron's decision tonight is in the best interests of the Labour Party as well as his own family," he said.
The Tory spokesman on constitutional affairs, Liam Fox, said he believed Mr Davies's decision had become inevitable.
"The Labour Party now have a political vacuum in Wales to fill," he said.
Mr Davies's spokesman said last night: "He has reached the decision in the interests of the Labour Party, the Assembly and above all, his family."
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