The broadcaster, who has presented the show for 25 years, said he wanted to "go to bed at much the same time as most people." He will leave in June but will continue to front University Challenge on BBC2.
He said: "This was a decision I reached — and informed the BBC of — last July. I shall work out the remainder of my contract and will not seek another. It's been fun. I have had the pleasure of working with lots of clever, creative and amusing people.
"I think I've been lucky and wish the programme well."
Occasional presenter Laura Kuenssberg, previously ITV's business editor, is the bookies' favourite to replace him, with fellow Scots Kirsty Wark and Eddie Mair also given strong odds.
The BBC said Leeds-born Paxman, whose ancestors lived in Glasgow, had agreed to stay to help its new editor "following a difficult period" which saw the show lambasted after it pulled a planned expose of Jimmy Savile's sex crimes.
Newsnight boss Ian Katz has also been forced to defend presenter Wark dancing to Michael Jackson's Thriller, and faced criticism over an edition which saw Emily Maitlis "interviewing" the Cookie Monster.
BBC Director-general Tony Hall described Paxman as a "rare and dazzling talent." He added: "He has a unique ability to create moments of real discomfort for politicians and memorable delight for audiences. For that cussed brilliance and much more besides, the BBC and our audiences will always be in his debt."
The BBC's director of news, James Harding, said Paxman was the "great lion of BBC journalism."