Tony Hall, chief executive of the Royal Opera House, is to be appointed director-general of the BBC, the corporation reported on Thursday.
The 61-year-old, a former director of news at the BBC, will take up his post next March, succeeding George Entwistle who resigned earlier this month after just 54 days in the job.
Lord Patten, the chairman of the BBC Trust, said Lord Hall's background in news "will prove invaluable as the BBC looks to rebuild both its reputation in this area and the trust of audiences".
Hall collecting his CBE in 2006
He added that he was the "right person" to lead the BBC as it takes "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 Hall said on Thursday: "I believe passionately in the BBC and that's why I have accepted Lord Patten's invitation to become director general."
He was appointed following a direct approach from the BBC Trust, which did not contact any other candidates. He was not an applicant when the position was vacated by Mark Thompson earlier this year.
Lord Hall, who was made a cross-bench peer in 2010 as Lord Hall of Birkenhead, is also deputy chairman of Channel 4.
Tim Davie will remain as the acting director-general until he is able to take up his appointment next year.
Hall, then-chief executive of the Royal Opera House in London with Britain's Queen Elizabeth II watching a Royal Ballet Gala
Lord Hall said today: "I believe passionately in the BBC and that's why I have accepted Lord Patten's invitation to become director general."
He was appointed following a direct approach from the BBC Trust, which did not contact any other candidates. He was not an applicant when the position was vacated by Mark Thompson earlier this year.
The new director general joins at a time of crisis for the corporation which was precipitated by the Jimmy Savile abuse scandal, and a subsequent report on BBC2's Newsnight programme which mistakenly implicated Lord McAlpine in child abuse.
That mistake led to Mr Entwistle quitting his post and also saw the BBC settling with Lord McAlpine for £185,000 last week.
Public trust in the BBC is said to have been knocked by the furore and a number of inquiries are under way into the fallout from the Savile problems.
Hall, receiving a Classic FM Innovation Award in 2009
Lord Hall will be paid £450,000 in the role - the same level of salary as his predecessor - and his appointment was unanimously agreed by Trustees this morning.
Lord Patten said: "While there are still very serious questions to be answered by the ongoing inquiries, it is in the interests of licence fee-payers that the BBC now starts to refocus on its main purpose - making great programmes that audiences love and trust.
"In doing this, it will need 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. Tony Hall is the right person to lead this and I am delighted that he is taking on this role.
"For its part, I want to make sure that the Trust gives Tony Hall whatever help and support he needs to re-build the BBC's management around him.
"Tony Hall has been an insider and is a currently an outsider. 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, who was head of BBC news and current affairs from 1996 to 2001 when he headed to the Royal Opera House, acknowledged it had been a "difficult few weeks" but said he wanted to lead a "world-class BBC".
He 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. I'm committed to ensuring our news services are the best in the world.
"I'm committed to making this a place where creative people, the best and the brightest, want to work.
"And I know from my first days here as a news trainee, to my time as head of news and current affairs, to my time now at the Royal Opera House, that I can't do it on my own.
"Having the right teams working together, sparking off each other, is key. And I want to build a world-class team to lead a world-class BBC."
Culture Secretary Maria Miller said: "I congratulate Tony Hall on his appointment as director general. He has a very strong track record in successfully leading iconic organisations.
""I am pleased the BBC Trust have appointed a new director general. 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."
Lord Hall's appointment was approved on the same morning BBC Trustee Anthony Fry was justifying the decision to give Mr Entwistle his full year's pay-off of £450,000 following his resignation.
He was appearing before the Public Accounts Committee and insisted it was the right thing to do to avoid a protracted legal wrangle.
The direct approach for Lord Hall's recruitment is a marked contrast to the team of headhunters that was involved in drawing up the list of candidates which resulted in Mr Entwistle being given the post.
Speaking about the latest appointment, Lord Patten said: "Just over four months ago the Trust completed a thorough recruitment process. Tony Hall wasn't available then but I am delighted he has agreed to come on board now.
"Of course, we might have considered going through the whole lengthy recruitment process again with a new round of advertisements and another global hunt for candidates.
"But I believe the approach we have taken is ultimately in the interests of the BBC and, most importantly, licence fee-payers as we have got the best candidate and he will help the organisation quickly get back on an even keel."
Birkenhead-born Lord Hall, who began as a news trainee with the BBC 39 years ago, is thought to have been in the running for the director general post when Greg Dyke was appointed in 1999.
The appointment will be welcomed by many at the BBC, according to respected broadcaster David Dimbleby.
He told the Press Association: "I think it's a very good choice and a great relief for those of us who work for the BBC.
"He knows the BBC and he's worked outside but, above all, he understands BBC journalism.
"He's a good public face for the BBC and I feel like I'm serving in the Royal Navy when the message came in: 'Winston is back'."
Dimbleby went on: "I think most people will be thrilled at this choice and will also get the leadership that is needed from somebody who is a creative man and a good administrator - and a calm man in a time of crisis."
Earlier, Dimbleby complained the BBC is "still over-managed and the management still speak gobbledegook", during an interview on Radio 4's Today programme in the wake of Mr Entwistle's departure.