The 62-year-old chief executive of the Royal Opera House has already held a news conference alongside the BBC Trust chairman Lord Patten at New Broadcasting House in central London.
He said that he is "passionate" about the BBC, but faces big challenges as the corporation's reputation is at an all time low following the Jimmy Savile sex abuse scandal.
Lord Hall is to start at the BBC in March next year, succeeding the short-lived tenure of George Entwistle, who quit over a Newsnight report that led to a senior Tory politician being wrongly linked to child abuse.
Former BBC Vision director Entwistle lasted just 54 days in the job, but walked away with a controversial £450,000 pay-off.
Culture secretary Maria Miller offered her congratulations to Lord Hall on his appointment as director general, and praised his "very strong track record in successfully leading iconic organisations".
"I am pleased the BBC Trust have appointed a new director general," she said. "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."
Professor Roy Greenslade noted that Lord Hall has the right combination of insider/outsider, as he spent five years at the BBC between 1996 to 2001 as head of BBC News and Current Affairs.
"I think he covers both essential facets of what you need in a director general," said the Guardian columnist. "He has news experience - which will be essential to clean up this Newsnight mess - and he has business experience at the Royal Opera House."
Just like others, Peter Snow noted that Lord Hall has done an "incredible job" at the Royal Opera House, as he arrived more than ten years ago when the institution was in crisis.
"He's tough, he's very approachable and accessible, easy to get on with but he's tough, he's a rigorous journalist too," he told the BBC.
"Here's a guy who's been the top journalist in many ways in the BBC, back when he was director of news - and now he's done an incredible job at the Royal Opera House, putting it back on its feet again after the shambles it was in back in the year 2000 or so when he went - so I think he's a terrific appointment."
Royal Opera House music director Antonio Pappano said that Lord Hall had been a "wonderful advocate" for the arts institution.
"He's been a great friend and colleague and while this is a fantastic opportunity for him to return to the BBC, and I can think of no better person for the BBC, we will miss him hugely here," he said.
Stephen Fry tweeted his approval for the appointment, saying: "I think Tony Hall is a really good DG choice, TBH. He's not a 'process' man, he's behind the best of BBC's digital moves in the past. Hope!"
Ian Burrell, the media editor for the Independent, has run a profile of Lord Hall, describing him as 'the arts grandee who ticks all the BBC boxes'.
Meanwhile, former BBC deputy director general Mark Byford said: "He has huge ability in journalism with extraordinary courage and wise judgement.
"He's got formidable intellect, he's also worked outside the BBC at the Royal Opera House with an outstanding track record there, and recently done the cultural Olympics as a very collaborative chair. I think he's the ideal candidate for the moment, and I wish him all the very best."
BBC Trust chairman Lord Patten has confirmed that Hall was the only candidate they contacted after Entwistle's resignation.
He said that the BBC previously approached him in the search after Mark Thompson announced his intention to step down earlier this year, but the Cultural Olympiad chairman turned down the chance at the time.
"When we talked at that stage he was involved in the Cultural Olympiad," Lord Patten said.
"He said he'd loved his time at the BBC but maybe a younger person should do the job. Clearly by this November things had changed substantially."
However, Hall was also turned down for the BBC director general job in 1999 when Greg Dyke was hired.
Former Sky and ITV executive David Elstein has questioned the merits of going back to a past candidate.
"Tony's an excellent person, who was turned down for the job in 1999 when Greg Dyke was selected, and who couldn't be bothered to apply for the job last time, which is only eight months ago," he said.
"Moreover, [it] wasn't thought worthy of approaching him, being offered the job then. He's passed the BBC retirement age. I mean, it's just a sign of how hopeless the BBC Trust and its chairman are."
Sir Christopher Meyer, the former chairman of the Press Complaints Commission, also tweeted: "Such an effusion of praise for Tony Hall, why didn't he succeed Mark Thompson in the first place?"
But former ITN chief executive Stewart Purvis said that the fact Lord Hall has been linked with the job in the past was not a bad thing.
"The fact that we believe he didn't apply first time around made him a very good candidate second time around, because he wasn't in any way damaged by the first time," he said.
"I would guess that perhaps the BBC Trust made it clear they would really like him to have the job - and being a BBC man at heart it was difficult to resist the temptation to come back and help at a difficult time."
Members of the public have also responded to the appointment. In the comments on Digital Spy's article, Sandra Perkins commented: "Yet another Man, havent they made enough of a mess of it already? (sic)"
In response to the BBC article, one contributor called "Phil" posted: "Dear BBC, Just make sure he can be fired for less than a million should he prove incompetent, please. Kind Regards, A Licence Fee Payer."