The former director of news at the BBC will take up his post next March, succeeding George Entwistle who resigned earlier this month after just 54 days in the job.
Tim Davie will remain as Acting Director-General in the interim period.
The new director general joins at a time of crisis for the corporation which was precipitated by the Jimmy Savile abuse scandal, and a subsequent report on BBC2's Newsnight programme which mistakenly implicated Lord McAlpine in child abuse.
Entwistle left his job on 10 November after a Newsnight report into child abuse allegations in North Wales was found to have incorrectly named the Tory peer.
Public trust in the BBC is said to have been knocked by the furore and a number of inquiries are under way into the fallout from the Savile problems.
Lord Hall will be paid £450,000 (€550,000) in the role - the same level of salary as his predecessor - and his appointment was unanimously agreed by Trustees this morning.
BBC Trust Chairman Lord Patten said: "While there are still very serious questions to be answered by the on-going inquiries, it is in the interests of licence fee payers that the BBC now starts to refocus on its main purpose – making great programmes that audiences love and trust.
"In doing this it will need 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. Tony Hall is the right person to lead this and I am delighted that he is taking on this role. For its part I want to make sure that the Trust gives Tony Hall whatever help and support he needs to re-build the BBC's management around him.
"Tony Hall has been an insider and is a currently an outsider. As an ex-BBC man he understands how the Corporation's culture and behaviour make it, at its best, the greatest broadcaster in the world. And from his vantage point outside the BBC, he understands the sometimes justified criticisms of the Corporation – that it can be inward looking and on occasions too institutional.
"But perhaps most importantly, given where we now find ourselves, his background in news will prove invaluable as the BBC looks to rebuild both its reputation in this area and the trust of audiences."