Announcing the appointment, BBC Trust chairman Chris Patten said Hall was "the right person to lead the BBC out of its current crisis".
Hall, 61, who will assume charge next March, said he was "committed to ensuring our news services are the best in the world".
His appointment follows the resignation of George Entwistle earlier this month after just 54 days in the job.
Entwistle quit on November 10, 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, Alistair McAlpine, being wrongly accused of child abuse.
The BBC had to publicly apologise for the error and paid McAlpine 185,000 pounds plus legal costs to settle a libel claim.
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 pounds a year, the BBC reported.
More From This Section
Hall also has the credentials of an insider, having led BBC News and Current Affairs from 1996 to 2001, during which he launched BBC News Online, Radio 5 Live and other channels.
British Culture Secretary Maria Miller offered her congratulations, saying Hall had "a very strong track record in successfully leading iconic organisations".
"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," she said.
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."
Hall 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.
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," he said.
When Entwistle quit, the BBC had already spent several weeks at the centre of a scandal over alleged 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.