Hall is expected to start in early March 2013 and Tim Davie, the BBC’s former head of audio and music and incoming chief executive of BBC Worldwide, will continue as acting director general until then.
Entwistle resigned from the BBC amid an escalating crisis following a ‘Newsnight’ film falsely implicating a former politician in a child abuse scandal, and the concern over the BBC’s decision to shelve an investigation into Jimmy Saville.
A cross-bench peer, Lord Hall of Birkenhead has been chief executive of the Royal Opera House since April 2001, was on the board of the London Organising Committee for the Olympic Games, and is currently deputy chairman of Channel 4.
At the BBC for 28 years from 1973, Hall held senior roles including senior producer of ‘World at One’, assistant editor of the ‘Nine O’Clock News’, and output editor for ‘Newsnight’, before becoming chief executive of BBC News in 1996.
Lord Patten, chairman of the BBC Trust said: "While there are still very serious questions to be answered by the ongoing 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 rebuild 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."
Hall will be paid £450,000 per year, the same salary as Entwistle.
Maria Miller, culture secretary, said: "Tony Hall has a very strong track record in successfully leading iconic organisations.
"I am pleased the BBC Trust has 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."
Hall will be required to stand down from his role as deputy chairman at Channel 4 when he takes up the post of director general.