He is expected to start in the role in early March 2013 and incoming BBC Worldwide chief executive Tim Davie will reman as acting director general in the interim.
[New BBC DG Tony Hall]
Lord Hall of Birkenhead, who will be paid £450,000 a year in the job, the same salary as earned by Entwistle, said that he "believes passionately" in the BBC.
Entwistle quit on November 10 after a disastrous Newsnight report led to Lord McAlpine being wrongly linked to alleged child abuse. Former BBC Vision director Entwistle lasted just 54 days in the role, the shortest ever reign for a BBC director general.
Ofcom chief executive Ed Richards and Channel 4 boss David Abraham were thought to be among candidates to take on the job permanently, but BBC Trust chairman Lord Patten has instead opted for Lord Hall.
Currently chief executive of the Royal Opera House, Lord Hall was chairman of the board for the Cultural Olympiad, and previously was head of BBC News and Current Affairs from 1996 to 2001.
In his past stint at the BBC, he helped launch BBC News Online, along with Radio 5 Live, BBC News 24 and BBC Parliament. Currently, he is deputy chair of Channel 4.
Lord Hall was approached directly by the BBC Trust and was the only candidate contacted about the director general role, according to the Trust.
[Former BBC DG George Entwistle]
Lord Patten said that his appointment was unanimously agreed by BBC Trustees at a meeting this morning.
"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," he said.
"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."
The appointment of Lord Hall comes at a time when the BBC's reputation is close to rock bottom, following shocking revelations about alleged sex abuse by former BBC star Jimmy Savile.
Two major independent investigations are currently being run into the culture of the BBC while Savile worked there and the decision to drop a Newsnight investigation into allegations Savile was a paedophile.
Lord Patten said that Lord Hall fits the bill to become the next BBC director general as he "has been an insider and is 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," said Lord Patten.
"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."
Lord Hall said that he "believes passionately in the BBC" and that is why he has agreed to take on the huge challenge of becoming its next director general.
"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," he said.
"It's been a difficult few weeks - but together we'll get through it. I'm committed to ensuring our news services are the best in the world. I'm committed to making this a place where creative people, the best and the brightest, want to work."
> George Entwistle 'wanted £450,000 pay-off to leave'