A radical "structural overhaul" of the BBC is necessary after the resignation of the director general, BBC Trust chairman Lord Patten has said.
George Entwistle quit on Saturday after a controversial Newsnight report led to a former Tory treasurer being wrongly accused as a child abuser.
He will receive a year's salary - £450,000 - as part of a pay-off.
The BBC Trust said acting director general Tim Davie would set out his initial plans on Monday.
The BBC's Norman Smith says the Trust had confirmed Mr Entwistle will be given a year's salary, even though he was legally only entitled to six months pay.
Our correspondent says it is understood the decision to give him a full year's salary was taken on Saturday night in order to reach a swift resolution to his departure.
Lord Patten has said a new director general would be chosen within weeks.
The BBC Trust said on Sunday night that it had had a discussion with Mr Davie and was "looking forward" to him setting out his plans for dealing with some of the issues arising from the 2 November Newsnight broadcast on Monday "as a first step in restoring public confidence".
Before his departure, Mr Entwistle had commissioned a report from BBC Scotland director Ken MacQuarrie into what happened with the Newsnight investigation. He was expected to report to the BBC on Sunday.
On 2 November Newsnight reported abuse victim Steve Messham's claims against a leading 1980s Tory politician being an abuser in north Wales, 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. He said the claims were "wholly false and seriously defamatory".
Lord Patten, told the BBC's Andrew Marr programme, he had to show licence fee-payers "that the BBC has a grip, that we get ourselves back on the road".
Of Mr Entwistle's departure, he said: "He's editor-in-chief of a great news organisation and I think he felt he should take responsibility for the awful journalism which disfigured that Newsnight programme [on 2 November].
"And one of the ironies is that he was a brilliantly successful editor of Newsnight himself for some time."
Mr Entwistle lasted just 54 days on the job, but Lord Patten praised him as "a very, very good man, cerebral, decent, honourable, brave".
He said it was too soon to talk of cutting Newsnight but said there was an "argument" for the BBC to look at giving the head of news a stronger role.
"I don't think you would ever want a situation in which there wasn't one person who was the boss - primus inter pares [first among equals]. But I do think you need to look at the relationship between the director general of the organisation, editorial and creative and I think that anybody but an archangel needs strong support in those areas."
BBC News management has not responded to requests for comment.
Downing Street sources say the prime minister believes the situation is "very difficult, very serious" but the BBC has the capacity to reform itself and to address failings.
Mr Cameron believes the BBC needs to "show grip" and Lord Patten "has started to make the right noises," they added.
In a tweet, Labour leader Ed Miliband said the BBC needed to put reforms in place and recruit a "strong" director general. He said it was "essential to restore trust in one of our great national assets".
Mr Entwistle was criticised for not knowing about the north Wales programme until after it screened, for not being aware of a newspaper article which revealed the mistaken identity, and for not knowing about a tweet saying Newsnight was poised to broadcast the revelations.
Lord Patten said he was aware of the tweet, which mentioned Conservative politicians, but said it would have been "grotesque interference" if he had contacted the programme then.
"I did subsequently ask whether the programme was being properly edited, whether it was being managed, and I was assured that it was."
Mr Entwistle had said the report had gone through management and legal checks before broadcast.
Mr MacQuarrie's report is not the only inquiry into Newsnight.
One inquiry is examining whether there were BBC management failings surrounding the decision not to broadcast a Newsnight programme about sex abuse claims surrounding the late BBC presenter Jimmy Savile.
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.
In the wake of the Newsnight Savile row, several senior news managers stepped aside from certain responsibilities while investigations took place.
In an email to staff after Mr Entwistle resigned, Lord Patten said the "priority now is to address the very serious questions that still remain around the original decision not to pursue the initial Newsnight investigation, how last week's story went so horribly wrong and, most importantly, how the BBC's historic culture and behaviour allowed Jimmy Savile to get away with his vile criminal activity".
Home Secretary Theresa May told Marr it was the right decision for Mr Entwistle to go.
"At the core of question about the Newsnight piece on north Wales is a question about the quality of journalism... I think the BBC has got a job to do to restore that trust."
She said two inquiries she announced last week into the abuse claims - one reviewing the Waterhouse Review into the original 1990s claims, and one looking at the police handling of the historic claims as well as fresh allegations - would continue.
Labour's deputy leader Harriet Harman said Mr Entwistle had not shown "clear leadership" but there was "such a depth of support and admiration and commitment" for the BBC from its staff and the public.
Guardian columnist Polly Toynbee said BBC journalism was "second to none, it is more trusted than anyone else" but a "bad mistake" had been made with the Newsnight story.
Former culture minister Kim Howells called for the resignations of Lord Patten and the BBC director of news, Helen Boaden.
He told BBC Wales' Sunday Supplement Programme: "Unfortunately there is a culture at the top of the BBC that is vain and out of touch. It's not doing what it should be doing which is supporting and encouraging muscular investigative journalism of the highest quality."