Lord Hall said the decision had been hard, adding: “If I followed my heart I would genuinely never want to leave.”
But he said he felt it was important the BBC had the same leader for the BBC’s mid-term review in 2022 and the renewal of its charter in 2027.
Sir David said the search for a new director general would begin “within the next few weeks”.
He added that the BBC was “committed to selecting the best qualified person for the job”.
Speaking of Lord Hall, he said the corporation had been “lucky to have him”.
He described him as “an inspirational creative leader” who had “led the BBC with integrity and a passion for our values”.
In a letter to staff, Lord Hall said he believed he would be “leaving the BBC in a much stronger place than when I joined”.
His appointment in 2012 followed the resignation of George Entwistle in the wake of the Newsnight Lord McAlpine row.
Hall’s departure comes amid another turbulent time for the broadcaster, with issues around equal pay disputes, political bias, diversity and TV licences at the top of its agenda.
Last week he outlined a plan that will see at least two thirds of the corporation’s staff based outside London by 2027.
Hall, 68, joined the corporation as a trainee in the Belfast newsroom in 1973.
He became editor of the Nine O’Clock News at the age of 34 and was appointed chief executive of BBC News in 1996.
Before becoming the BBC’s 16th director general, his roles included being chief executive of the Royal Opera House and deputy chairman of Channel 4.
Hall, whose official title is Lord Hall of Birkenhead, was made a cross-bench peer in 2010.
Bonnie Greer, who served alongside Hall on the Royal Opera House board, noted that the BBC had been going through a difficult period.
“I think it’s been a lot of pressure for the organisation and a lot of pressure for him,” the playwright and critic said on The Victoria Derbyshire Show.
Talent agent Jonathan Shalit said Hall had been “fantastic” in the director general role and that it was “normal” for someone in his position to move on after seven years.
“He was going to be moving on soon,” he told the same BBC programme. “I think the point he makes about making sure one person oversees the midway point of the licence fee is important.”
The DTG has a wealth of resources available to its Members which includes reports, papers, infographics and presentations. We also have an extensive DTG Archive which covers broadcast industry developments over almost a quarter of a century. However some DTG publications are available by email on a complimentary basis.Find Out More
The DTG Bulletin is a weekly curation of industry news and events with informed comment from DTG industry experts and Members. It also includes details of Member Offers which entitle DTG Members to discounts. To register your interest in receiving the DTG Bulletin please click the button below.Sign up Today