Entwistle – who had been director general for less than two months – said he had decided that "the honourable thing to do" was to step down. It follows a torrid week for the BBC which has been mired in crisis since the Jimmy Savile scandal first erupted.
His resignation came less than 24 hours after Entwistle gave an excruciating performance on Radio 4's Today programme when he admitted he was completely unaware of the Newsnight report that wrongly implicated the former Tory treasurer Lord McAlpine in child abuse allegations until the day following its broadcast.
Despite a tweet before the Newsnight broadcast that suggested the programme was going to identify a senior political figure attracting widespread interest, the former director general said he only found out about the film after it had been broadcast. The Newsnight programme went out on Friday, November 2, but Entwistle said he was "out" when it was broadcast.
Reading a prepared statement outside New Broadcasting House, shortly after 9pm last night, Entwistle said the "wholly exceptional" events of the last week had convinced him he should stand down.
"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 on Friday, November 2, I have decided that the honourable thing to do is to step down from the post of director general.
"When appointed to the role, with 23 years' experience as a producer and leader at the BBC, I was confident the trustees had chosen the best candidate for the post, and the right person to tackle the challenges and opportunities ahead.
"However, the wholly exceptional events of the last few weeks have led me to conclude that the BBC should appoint a new leader. To have been the director general of the BBC even for a short period, and in the most challenging of circumstances, has been a great honour.
"While there is understandable public concern over a number of issues well covered in the media – which I'm confident will be addressed by the review process – we must not lose sight of the fact that the BBC is full of people of the greatest talent and the highest integrity. That's what will continue to make it the finest broadcaster in the world."
BBC Trust chairman Lord Patten, who made a statement following Entwistle's resignation, paying tribute to the former director general, said: "This is undoubtedly one of the saddest evenings of my public life ... George has very honourably offered his resignation because of the unacceptably shoddy journalism which has caused so much controversy."
Tim Davie, recently appointed as chief executive of BBC Worldwide, is to lead the organisation as the search for Entwistle's replacement gets under way.
Prior to his resignation, Entwistle had described the story on the North Wales children's home scandal, which led to false rumours about McAlpine being widely circulated on the internet, as "fundamentally wrong".
It also earlier emerged that no member of the BBC team, which was working with the not-for-profit Bureau of Investigative Journalism, attempted to contact McAlpine about the story prior to broadcast.
The BBC was forced to issue an unreserved apology after one of the victims spoken to for the programme admitted he wrongly identified McAlpine as his abuser during the 1970s and 1980s. Steve Messham says no member of the BBC team showed him a picture of McAlpine throughout the investigation.
Although the programme did not name McAlpine, the peer has indicated he now intends to sue the BBC after it led to him being identified on the internet.
In the run-up to his resignation, Entwistle was likened to "man in a pit digging himself even deeper" as he struggled to contain the damage over the crisis. Entwistle – himself a former Newsnight editor – said he only became involved in editorial decisions if a programme was referred to him for attention, and the BBC would not work if he had to "pore over" all ongoing investigations.
Entwistle had also said he was unaware of newspaper reports on Friday that first suggested McAlpine had been a victim of mistaken identity, because he was making a speech.
Before he quit, Entwistle asked the director of BBC Scotland, Ken MacQuarrie, to investigate the Newsnight story and report on the findings by today, with staff potentially facing disciplinary action. MacQuarrie was previously given the task of talking to Newsnight journalists who had raised concerns over the dropping of the Newsnight Savile investigation.
Earlier on Saturday, Entwistle insisted he had no intention of resigning, although he did say that his future lay in the hands of the BBC Trust.
All investigations by Newsnight have now been halted while their journalistic robustness is checked. The BBC has also suspended all co-productions with the Bureau of Investigative Journalism.
Entwistle rejected suggestions that the BBC's flagship current affairs programme – first broadcast in its current format in 1980 – should be axed.
Before his resignation, a number of senior figures turned on Entwistle. Newsnight's founding editor George Carey accused him of showing an "astonishing lack of curiosity".
Tory MP Rob Wilson, a prominent critic of the BBC over the Savile affair, said: "I think there are questions for George Entwistle about whether he is the right person to lead the BBC out of the difficulty and the crisis it finds itself in."
Another Tory MP, John Whittingdale, chairman of the Commons Culture, Media and Sport Committee, said: "It is hard to imagine a more damaging, appalling allegation than to label somebody as a child abuser. At the end of the day, the director general of the BBC is editor-in-chief. I would have expected a programme making as serious allegations as these to have gone to him for clearance."
Culture Secretary Maria Miller said events of the past days underlined the "vital importance of restoring credibility" in the corporation.
PROFILE: GEORGE ENTWISTLE
After studying philosophy and politics at Durham University and a period in magazine journalism, George Entwistle joined the BBC in 1989 as a broadcast journalism trainee. He served as an assistant producer on Panorama, where he worked on the programme's coverage of events including the first Gulf War. In January 1993, he served as a producer for On The Record and subsequently served as a producer, assistant editor and deputy editor of BBC Two's current affairs flagship, Newsnight. Entwistle served as an editor of Newsnight in 2001. In 2004, he left Newsnight for BBC Arts and served as an executive editor of Topical Arts on BBC Two and BBC Four. Since 2005, he served as head and commissioning editor of TV Current Affairs and joined BBC Television's factual commissioning team. Entwistle also commissioned a wide variety of current affairs documentary series for BBC Two, including The Conspiracy Files, Michael Cockerell's series Blair: The Inside Story, and Tropic Of Capricorn with Simon Reeve. On July 4, 2012, the chairman of the BBC Trust, Lord Patten, announced that Entwistle had been appointed to succeed Mark Thompson as director general of the BBC. His resignation is the latest among a number of directors general who have resigned, including Alasdair Milne and Greg Dyke.