The head of the Royal Opera House, Tony Hall, has been given the biggest job in broadcasting after being appointed BBC director-general as the corporation acted quickly to move on from its crisis.

He was handed the £450,000-a-year role after being directly approached by the BBC Trust, only 12 days since George Entwistle resigned from the post 54 days into his role.

The appointment of Lord Hall, a former BBC news executive who has been chief executive of the ROH since 2001, has been widely hailed for giving the corporation some welcome leadership. Tim Davie will remain as the acting director-general until Lord Hall is able to take up the post next March.

Lord Patten, chairman of the BBC Trust, said Lord Hall 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".

The new director-general - who was the only candidate contacted by the Trust - said: "I believe passionately in the BBC and that's why I have accepted Lord Patten's invitation to become director-general."

The 61-year-old - made a cross-bench peer in 2010 - has retained his interests in broadcasting as deputy chairman of Channel 4. Culture Secretary Maria Miller said: "He has a very strong track record in successfully leading iconic organisations."

Lord Hall will have to rebuild the BBC's battered reputation after weeks of difficulties 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.

Lord Patten said of the fast-track appointment, unanimously agreed by trustees: "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."

Speaking at a press conference, Lord Hall said: "It takes a lot to drag me away from the Royal Opera House Covent Garden, a place I love hugely. But the reason I am standing before you today is because I care passionately about the BBC, about what it can do, its programme-makers and the impact we have in all sorts of different ways.

"(It is) One of those extraordinary organisations which is an absolutely essential part of the UK, of Britain, of who we are. But also it has this incredible impact around the world too."