Mr Entwistle, who took over as the organisation's leader only 54 days ago, said the "wholly exceptional" events of last week had convinced him he should stand down.
He fell on his sword over the "unacceptable" Newsnight broadcast eight days which wrongly implicated a senior former Conservative in a child abuse scandal in Wales.
Yesterday, it emerged that a victim featured in the programme ruled out the involvement of Lord McAlpine, once a party deputy treasurer, whose name had been wrongly linked to the story on Twitter after the Newsnight report.
The BBC2 programme had to broadcast an embarrassing apology at the start of last night's programme and Mr Entwistle admitted earlier today he had not seen or been told of the report before it was aired.
That led to a fresh barrage of criticisms from leading political figures who argued that the corporation's global reputation for being trusted had been severely damaged by its internal procedures.
The BBC was already badly scarred by the decision not to broadcast an investigation into Jimmy Savile's abuses, which was then covered on ITV.
Tonight, in a brief statement outside Broadcasting House, Mr Entwistle said that he had decided to do the "honourable thing" and step down from his post.
"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," he said.
"However the wholly exceptional events of the past few weeks have led me to conclude that the BBC should appoint a new leader."
Standing alongside him, the chairman of the BBC Trust, Lord Patten, said it was "one of the saddest evenings of my public life".
"At the heart of the BBC is its role as a trusted global news organisation," he said.
"As the editor in chief of that news organisation George has very honourably offered us his resignation because of the unacceptable mistakes - the unacceptable shoddy journalism - which has caused us so much controversy.
"He has behaved as editor with huge honour and courage and would that the rest of the world always behaved the same."
Seconds before Mr Entwistle stepped outside to face the cameras and resign as director general, he pressed the button on an email to BBC staff explaining his action.
In the message, the ex-editor-in-chief wrote that the public's confidence in the corporation was damaged but stressed the BBC was still full of staff of integrity and talent.
He wrote: "Dear All, The circumstances of the past few weeks, and in particular the unacceptable journalistic standards of the Newsnight film that was broadcast on Friday 2nd November, have damaged the public's confidence in the BBC.
"As the Director-General of the BBC, I am ultimately responsible for all content as the Editor-In-Chief, and I have therefore decided that the honourable thing for me to do is to step down.
"When appointed to this role, with 23 years' experience as a producer and leader at the BBC, I was confident that I was the best candidate for the post, and the right person to tackle the challenges and opportunities ahead.
"However the exceptional events of the past 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 circumstances, has been a great honour, and I am pleased to have had that opportunity.
"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 - I hope you will 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 ensure it continues to be the finest broadcaster in the world. All the best, George."
Tim Davie, chief executive of BBC Worldwide and regarded as a relatively independent figure who has not been involved in recent journalistic events, has been appointed as acting DG.
Mr Entwistle's association with the corporation goes back to when he was just six-years-old.
The schoolboy penned a letter then to the man then running the Corporation, complaining that Tom and Jerry had been bumped off the schedule.
Forty-four years on it was the bumping off the schedule of the Newsnight Jimmy Savile expose that spelt trouble for the editor-in-chief.
After weeks of damaging headlines about editorial failings and lapses in managerial judgment the pressure was building on Mr Entwistle.
And after being forced to apologise for the second Newsnight mess in which the flagship programme falsely implicated Lord McAlpine in a child abuse scandal, Mr Entwistle was left battling for his job.
He tried to explain his stance and answer tough questions on BBC Breakfast today but was left reeling with an excoriating interview on another BBC flagship - BBC Radio 4's Today programme - in which he was roasted by veteran journalist John Humphrys.
It was all too much and Mr Entwistle's stint as director general was over in less than two months.
Mr Entwistle, 50, took over as director-general from Mark Thompson on a much-reduced salary of £450,000.
He told the Radio Times that his father, a lecturer, did not send the letter complaining about the cartoon but handed it to his son more than 40 years later, when he applied for the high-profile job of running the BBC. "I had misspelt it 'derector'.
"My father, underneath, had written Broadcasting House, London, and then failed to post it - very typical of my dad," Mr Entwistle revealed.
The outraged six-year-old wrote the letter on behalf of his two younger brothers when coverage of Chancellor Roy Jenkins' 1969 budget overran and cartoon Tom and Jerry disappeared from the schedule.
The former director of BBC Vision, who launched The Culture Show and edited Newsnight, was rejected by two BBC graduate training schemes before finally getting a foot in the door.
He told the magazine that he had been fascinated by culture and international politics from a young age, saying: "I would go to my bedroom and listen to Kaleidoscope and The World Tonight.
"I think my parents thought it was a bit strange. But these programmes laid a foundation..."
He added: "There has barely been a morning - with the exception of holidays - since I was aware of what was going on in the world, that I haven't listened to the Today programme."
In his first full day running Newsnight in 2001, the September 11 terror attacks took place.
"It's awful, in these tragic human events journalists can't quite get the excitement out of their voice about how it felt," he said.
He said of running the BBC: "The original letter I wrote as part of the application process (for the job of director-general) said that I both love the BBC and at times find it an immensely frustrating place."
He added: "My hunch is that there isn't a single bit of the BBC that, in places, can't do better."