He replaces George Entwistle, who resigned earlier this month after only 54 days in the position following the broadcast of an erroneous "Newsnight" report.
Acting director general Tim Davie will continue until Hall assumes the post in March.
BBC Trust Chairman Chris Patten said the BBC needs "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," he said.
"Tony Hall has been an insider and is currently an outsider. As an ex-BBC man he understands how the corporation's culture and behavior 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."
The shakeup at the BBC comes amid a scandal in which hundreds of women said former radio and TV personality Jimmy Savile, who died last year at age 84, sexually abused them when they were girls. Police and BBC investigations are currently under way.
Megyn Kelly: Santa Claus and Jesus are both white men
Video of Victoria’s Secret models trying to 'twerk' hits Instagram