Tony Hall, a former a former director of BBC news, will replace George Entwistle who resigned as director-general this month after failing to get to grips with a scandal that threw the 90-year-old state-funded organisation into turmoil.
Chris Patten, chairman of the BBC Trust which overseas the broadcaster and appoints its chief, said Hall was "the right person to lead the BBC out of its current crisis" and that his journalism experience would be "invaluable as the BBC looks to rebuild its reputation."
Hall, who will take up the role in March, left the BBC shortly after missing out on the top job in 2001.
His predecessor lasted just 54 days in the job, widely criticised for lacking leadership amid a scandal centring on the former BBC presenter Jimmy Savile, who died last year and has since been exposed as a predatory serial child abuser.
Already under fire for his handling of the Savile affair, Entwistle quit after the BBC's flagship programme "Newsnight" wrongly claimed a senior Conservative politician had also been involved in child sex abuse.
"The past eight weeks have been very traumatic for the BBC but this is a significant day ... (that) marks the beginning of a new phase," Patten said in a statement.
In early reaction, media analysts greeted the appointment of Hall as a sound choice.
"He is an insider in the sense that the BBC will not be strange to him, but he is an outsider in the sense that he has good experience of running quite a difficult public sector institution, and doing so rather well," said Steven Barnett, professor of communication at Westminster University.
Hall, he added, was "definitely someone who the BBC can rely on to get it out of the mess that it is in now."
Roy Greenslade, professor of journalism at City University, London said: "I'm delighted. I think he's a very wise appointment.
"He's a rare combination: someone who rose very high at the BBC, but who's also done well outside it.
"I think he covers both essential facets of what you need in a director-general. He has news experience - which will be essential to clean up this Newsnight mess - and he has business experience at the Royal Opera House."
John Whittingdale, chairman of parliament's media committee, said the Trust had been sensible to move quickly in making a new appointment but he questioned whether Hall would be able to deal with reforming BBC bureaucracy.
"The area where there does need to be strong leadership is in streamlining and getting to grips with the bureaucracy and structure within the BBC," Whittingdale told Reuters.
"That, possibly, is an area where Tony Hall doesn't have experience and there might have been a case for somebody with more external management experience."