The BBC's director general, George Entwistle, has resigned in the wake of the Newsnight child abuse broadcast.
He said that as the man "ultimately responsible for all content, and in the light of the unacceptable journalistic standards" he would quit.
Mr Entwistle had admitted Newsnight's report, which led to Thatcher-era Tory Lord McAlpine being wrongly implicated, should not have been aired.
The broadcast covered cases of child abuse at north Wales care homes.
BBC Trust chairman Lord Patten, who appeared alongside Mr Entwistle when he delivered his statement, will answer questions on the BBC's Andrew Marr programme on Sunday morning.
Mr Entwistle took up the post of director general on 17 September, and his sudden resignation makes him the shortest-serving BBC director general.
In his statement, 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 on Friday 2 November, I have decided that the honourable thing to do is to step down from the post of director general."
He said that when he was appointed to the role, he was confident BBC 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 past few weeks have led me to conclude that the BBC should appoint a new leader," he said.
"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.
"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."
Later, speaking outside his home following his resignation, Mr Entwistle said he was going to "spend some time with my family".
During his 54 days in charge, Mr Entwistle has also had to deal with controversy over the BBC shelving a Newsnight investigation into former BBC presenter and DJ Jimmy Savile, who police say could have abused as many as 300 people over a 40-year-period.
As a result, an inquiry is examining whether there were BBC management failings surrounding the Newsnight's Savile programme not being broadcast, and another inquiry has begun into the culture and practices at the BBC in the era of alleged sexual abuse by Savile. Another review is to examine sexual harassment policies at the BBC.
Mr Entwistle's resignation came after he was criticised for his performance during an interview on the BBC's Radio 4 Today programme on Saturday, in which he admitted he had not read a newspaper article revealing the case of mistaken identity involving Lord McAlpine, and that he had not seen the Newsnight broadcast when it aired on 2 November as he "was out".
Lord Patten said: "This is undoubtedly one of the saddest evenings of my public life."
He added: "At the heart of the BBC is its role as a trusted global news organisation.
"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."
Culture Secretary Maria Miller said: "It is a regrettable, but 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 programmes."
But Labour MP Ben Bradshaw, who sits on the culture select committee, said Mr Entwistle's departure was a "terrible mistake" and that he had been "hung out to dry".
He described Mr Entwistle as "an honourable, highly talented, very very good man who is trying to do the right thing".
"George Entwistle has been badly let down by BBC News managers and the people around him. He was trying to get to grips with that. The BBC should have given him time."
Conservative MP Philip Davies, who also sits on the culture select committee, said Lord Patten should resign. "He is responsible for the public's trust in the BBC," Mr Davies told the BBC. "That trust is at an all time low."
Tim Davie, director of BBC Audio and Music, will take over as acting director general immediately.
BBC home editor Mark Easton said the BBC was at a "real crossroads, because its whole future depends on convincing the public in the United Kingdom that this is an organisation in which they have confidence, and in which they have trust, and that they believe in the integrity of our news coverage".
BBC Newsnight presenter Jeremy Paxman said Mr Entwistle's departure was "a great shame."
"He has been brought low by cowards and incompetents."
Newsnight reported on 2 November abuse victim Steve Messham's claims against a leading 1980s Tory politician, but he withdrew his accusation a week later, saying he had been mistaken.
Lord McAlpine, although not named on Newsnight, was identified on the internet as the subject of the allegations.
Mr Messham apologised to Lord McAlpine saying he was not the man who assaulted him, while Lord McAlpine said the claims were "wholly false and seriously defamatory".
The BBC has ordered an "immediate pause" in Newsnight investigations to assess editorial robustness and a suspension of all co-productions with the Bureau of Investigative Journalism, which worked on the Newsnight broadcast.
Before his departure, Mr Entwistle had commissioned a report from BBC Scotland director Ken MacQuarrie into what happened with the Newsnight investigation.