In a brief statement outside BBC headquarters, George Entwistle said he decided to do the "honourable thing" and step down after just eight weeks in the job.
"The wholly exceptional events of the past few weeks have led me to conclude that the BBC should appoint a new leader," he said.
It was a rapid about-face for Entwistle, a 23-year BBC veteran who earlier Saturday had insisted he had no plans to resign despite growing questions about his leadership and the BBC's integrity in the wake of the scandals.
Lawmaker John Whittingdale, who chairs a parliamentary committee on the news media, said Entwistle had no choice but to go, as the BBC's management appears to have "lost their grip" on the publicly funded organization.
"I think that what has happened in the last few days has immensely weakened his authority and credibility," Whittingdale said. "It would have been very difficult for him to continue in those circumstances."
The scandal comes at a sensitive time for Britain's media establishment, struggling to recover from an ongoing phone-hacking scandal which brought down the nation's bestselling Sunday newspaper, led to the arrests of dozens of journalists and prompted a judge-led inquiry into journalistic ethics and the ties between politics and the news media.
Kevin Marsh, a former senior editor of the BBC, said the resignation does little to re-establish public trust in the BBC, which is funded mainly by a tax on U.K. households that have televisions.
"The BBC asks the British public to pay its bills every year, and the only way it can do that is if the British public trusts the way it is spending its money," he said.
Entwistle took over as head of the BBC two months ago from Mark Thompson, who will become chief executive of The New York Times Co. this month. The broadcaster was emerging from a difficult period marked by budget cuts, job losses and mounting calls to justify its 3.5 billion pound ($5.6 billion) budget.
A month into Entwistle's leadership, the BBC was thrown into crisis with the revelation that its "Newsnight" program had shelved an investigation into allegations that Jimmy Savile, the renowned BBC TV host who died last year, had sexually abused several hundred children — cajoling some into having sex with him in his car, his camper van, and even in dingy dressing rooms on BBC premises.
The sex allegations were later aired on the rival ITV network. Since then, scores of adults have come forward to claim that their allegations of sexual assault had been ignored by authorities and the news media.
The BBC's decision not to air the Savile report — and the suggestion that managers did not investigate allegations of sexual abuse by one of their stars — prompted deep soul-searching at the trusted broadcaster and assurances from Entwistle that he would get to the bottom of the decision.
He said the broadcaster would hold an inquiry into the "culture and practices of the BBC" during the years Savile worked there. Soon after, "Newsnight" editor Peter Rippon stepped aside pending an investigation into his decision to scrap the Savile story.
But the furor was reignited soon after the same program aired a Nov. 2 report about alleged sexual abuse of children in Wales in the 1970s and 1980s. During the program, victim Steve Messham claimed he had been abused by a senior Conservative Party figure.
The BBC didn't name the alleged abuser, but online rumours focused on Alistair McAlpine, a Conservative Party member of the House of Lords. On Friday, McAlpine issued a fierce denial and threatened to sue.
Messham then said he had been mistaken about his abuser's identity and apologized to McAlpine, prompting criticism over the BBC's decision to air the report, the suspension of investigative programs at "Newsnight" and mounting questions over Entwistle's leadership.
Entwistle insisted he was not aware of the program before it was broadcast, saying in hindsight he wished the matter had been referred to him. That claim drew incredulity from politicians and media watchers who wondered how he could have allowed a second botched handling of a high-profile child sex-abuse story only weeks after the Savile scandal.
When the Savile scandal broke, he had portrayed himself as a hands-off chief executive who relies on a BBC system under which issues are brought to his attention by competent editors and executives.
He pleaded the same in a combative BBC radio interview on Saturday, saying that the McAlpine report, as far as he could tell, had been referred to senior figures in the BBC's news, management and legal divisions.
Marsh, the former BBC editor, said Entwistle's position became untenable after those comments and appearances made clear the executive had no idea what was going on within his own organization.
"This was an absolutely catastrophic combination of events," he said. "He inherited a massive crisis over Jimmy Savile. He made some missteps in managing that. He then never corrected those missteps and that helped generate the Lord McAlpine crisis."
The BBC Trust's chairman, Chris Patten, called Saturday "one of the saddest evenings of my public life" but praised Entwistle's "honour and courage" in tendering his resignation.
"At the heart of the BBC is its role as a trusted global news organization, and as the editor-in-chief of this organization, George has very honourably offered us his resignation because of the unacceptable mistakes and the unacceptable shoddy journalism which has caused so much controversy," Patten said.
British Culture Secretary Maria Miller welcomed the resignation, calling it "regrettable but the right decision."
"It is vital that credibility and public trust in this important national institution is restored. It is now crucial that the BBC puts the systems in place to ensure it can make first-class news and current affairs programs," she said.
Media watchers say doing so could mean rethinking the management structure of the BBC, whose portfolio of radio and television channels dominate the British media landscape.
"The BBC has been run by too many people who are insiders and there's no clear chain of command," said Charlie Beckett, director of the London School of Economics think-tank Polis. "It has such a strong, closed-system culture that it needs an injection of fresh thinking."
Beckett noted that in the past, trust in the BBC has recovered from scandals because the broadcaster "provides so much to the public as individuals."
But journalists might be left in a more precarious position of lacking the confidence to do challenging investigative and critical journalism, Beckett said.
"The danger is that the BBC will play safe, and it's too important in British life for it to always play safe," Beckett said.
The chief executive of BBC Worldwide, Tim Davie, will serve as acting director general until a permanent replacement for Entwistle is found.
Associated Press writer Cassandra Vinograd can be reached at http://twitter.com/CassVinogradSuggest a correction