The chief executive of the Royal Opera House and the BBC's former director of news, Tony Hall, has been appointed the corporation's new director general.
BBC Trust chairman Lord Patten said Lord Hall was "the right person to lead the BBC out of its current crisis".
Lord Hall, who starts next March, said he was "committed to ensuring our news services are the best in the world".
The appointment follows the resignation of George Entwistle earlier this month after just 54 days in the job.
Mr Entwistle quit on 10 November, saying that as editor-in chief he had to take "ultimate responsibility" for a Newsnight investigation that had led to the former Conservative Party treasurer, Lord McAlpine, being wrongly accused of child abuse.
Sixty-one-year-old Lord Hall is due to take over the role - currently occupied by acting director general Tim Davie - in early March, on a salary of £450,000 a year.
Culture Secretary Maria Miller offered her congratulations, saying Lord Hall had "a very strong track record in successfully leading iconic organisations".
She added: "It is important now that Tony Hall gets to grips quickly - to provide the stability and certainty that the BBC needs, and restore public confidence."
'Long, hard look'
The BBC needed "to take a long, hard look at the way it operates and put in place the changes required to ensure it lives up to the standards that the public expects", Lord Patten said. "Tony Hall is the right person to lead this."
Tony Hall - Lord Hall of Birkenhead - had emerged in recent days as the clear favourite for the job of stabilising the BBC and leading it out of its current crisis.
He is an outsider - as Lord Patten, the chairman of the BBC Trust, said he wanted - but he also worked at the BBC for many years, latterly as director of BBC News, where he launched Radio 5 live and the BBC News Channel.
He is credited with helping turn round the Royal Opera House, which had been in crisis before he joined as chief executive, and also the Cultural Olympiad, which had been in similar difficulties.
Lord Patten said his experience as a former BBC journalist would prove invaluable as the BBC looked to rebuild its reputation in this area.
Read more from Torin
"As an ex-BBC man he understands how the corporation's culture and behaviour make it, at its best, the greatest broadcaster in the world.
"And from his vantage point outside the BBC, he understands the sometimes justified criticisms of the corporation - that it can be inward-looking and on occasions too institutional.
"But perhaps most importantly, given where we now find ourselves, his background in news will prove invaluable as the BBC looks to rebuild both its reputation in this area and the trust of audiences."
Lord Hall said: "This organisation is an incredibly important part of what makes the United Kingdom what it is. And of course it matters not just to people in this country - but to tens of millions around the world too.
"It's been a difficult few weeks - but together we'll get through it."
Lord Hall joined the BBC as a news trainee in 1973 and during his 28 year career at the corporation oversaw the launch of Radio 5 live, the BBC News Channel, the BBC News website and BBC Parliament. He began his job at the Royal Opera House in 2001.
In 2009 he joined the board of the organising committee for the London Olympics and also set up and chaired the board of the Games' arts festival, the Cultural Olympiad.
He was made a cross-bench peer in 2010 as Lord Hall of Birkenhead.
Lord Hall, who is currently deputy chairman of Channel 4 and sits on the board of the British Council, will be standing down from these roles before he takes up the post of director general.
Mr Entwistle resigned over a 2 November Newsnight report, about claims of child abuse at north Wales care homes, that he said was guilty of "unacceptable journalistic standards" and should not have aired.
At that time, the BBC had already spent several weeks at the centre of a scandal over sexual abuse carried out by the late DJ and TV presenter Jimmy Savile.
Police believe Savile may have abused 300 young people over a 40-year period.
Source BBC News