Tony Hall, Lord Hall of Birkenhead, is to be the new BBC director-general, taking up his post in March 2013. He replaces Tim Davie, who became acting DG following George Entwistle's resignation.
In a statement, the BBC Trust said: "The BBC Trust has today appointed Tony Hall - Lord Hall of Birkenhead - as the director-general of the BBC, following the departure of George Entwistle.
"Lord Hall is currently chief executive of the Royal Opera House, was chairman of the board for the cultural Olympiad and was head of BBC News and current affairs from 1996 to 2001.
"He was a digital pioneer, launching BBC News Online, as well as Radio 5 Live, BBC News 24 and BBC Parliament. At present he is deputy chairman of Channel 4."
Lord Hall takes up his post after a number of controversies involving the reporting and misreporting of child abuse scandals involving Jimmy Savile and Lord McAlpine - who was wrongly implicated in allegations - forced his predecessor George Entwistle to resign.
We have got the best candidate and he will help the organisation quickly get back on an even keel. Lord Patten
His annual salary will be £450,000, the BBC Trust said.
Culture Secretary Maria Miller urged Lord Hall to restore trust in the BBC: "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."
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.
Congrats to Tony Hall as new BBC DG, the third successive ex-Newsnight producer to get the job, and author of excellent book King Coal— Michael Crick (@MichaelLCrick) November 22, 2012