The 79-year-old presenter has been at the helm of the flagship BBC1 political programme since 1994 and will leave the show in December this year.
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Citing that it was "the right moment to leave", Dimbleby added that he was "not giving up broadcasting" and wanted to "return to my first love: reporting".
There have only been three presenters of Question Time since its inception in 1979: Robin Day, Peter Sissons and Dimbleby, who is the longest-serving presenter in the show's history.
Paying tribute, BBC director general Tony Hall said: "David has been at the helm of Question Time for over 25 years: a brilliant champion of the public and the audience's friend – getting the answers they want on the big and difficult issues of the day.
"Always a commanding figure, David has ensured Question Time has not only stayed relevant through the years, but a must watch for those interested in politics and current affairs.
"The BBC and the public are extraordinarily lucky to have him in what are – to say the least – interesting times politically and socially. We look forward to working with him on other projects in the future."
The question now is who Dimbleby's successor will be. Newsnight's Kirsty Wark recently said she would "throw her hat in the ring" if the job became available, while other speculated names include John Humphrys, Victoria Derbyshire, Nick Robinson and Huw Edwards.