In a statement given outside New Broadcasting House, Entwistle said: "I have decided that the honourable thing to do is to step down," BBC reported.
Entwistle said the Newsnight report, which wrongly implicated ex-senior Tory Lord McAlpine should never have been broadcast. It covered cases of child abuse at north Wales care homes.
In a statement given at 9.00 p.m., he said: "In the light of the fact that the director general is also the editor in chief and ultimately responsible for all content, and in the light of the unacceptable journalistic standards of the Newsnight film broadcast Friday Nov 2, I have decided that the honourable thing to do is to step down from the post of director general."
Entwistle said when he was appointed to the role, he was confident BBC trustees had chosen the best candidate for the post.
"However the wholly exceptional events of the past few weeks have led me to conclude that the BBC should appoint a new leader," he said.
With his sudden resignation, Entwistle, who took up the post of director general Sep 17, turned the shortest-ever serving BBC director general.
In an earlier report, an ex-Tory politician was accused of sex abuse by a victim (name withheld for legal reasons), who was shown a photo in the 1990s which led to his accusation, but found out Friday that he was accusing the wrong person.
Although not naming Lord McAlpine, the programme falsely hinted that the former Tory treasurer of the Margaret Thatcher era was the offender, Xinhua reported.
Entwistle offered his apology after the scandal, saying that the programme should not have been broadcast. He was, however, under fire for knowing nothing about the Newsnight report in advance.
This was the second occasion when Entwistle was caught in the mire recently, after Britain was stunned by the child abuse scandal by former TV presenter Jimmy Savile. He was then ridiculed for his ignorance.
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