The BBC said he made his decision last summer but "generously agreed" to stay until June to help the show through "a difficult period". That came after it chose not to run an item linking Jimmy Savile with child abuse.
Paxman said it was "time to move on" and he "should rather like to go to bed at much the same time as most people".
Director General Tony Hall said Paxman, 63, was "a rare and dazzling talent".
"He has a unique ability to create moments of real discomfort for politicians and memorable delight for audiences," Mr Hall said.
"For that cussed brilliance and much more besides, the BBC and our audiences will always be in his debt."
Paxman will continue to present University Challenge, which he has fronted since 1994.
The BBC's head of news, James Harding, said Paxman had become the "great lion of BBC journalism" who "never failed to ask the difficult questions".
Associate editor of the Daily Mirror Kevin Maguire tweeted: "Jeremy Paxman quitting Newsnight is like the ravens flying the Tower of London or the Barbary apes leaving Gibraltar."
And the Daily Telegraph's Dan Hodges wrote that the "great lion sleeps tonight", adding that "the place people now go at 10.30pm to get their current affairs fix isn't the TV, but Twitter".
Paxman, who previously worked on programmes including Panorama and BBC's Breakfast Time, is best known for his confrontational interview style.
Among his most famous grillings was that of Michael Howard in 1997, when he asked the Conservative politician the same question 12 times.
Former home secretary Mr Howard had held a meeting with Derek Lewis, the head of Her Majesty's Prison Service about the possible dismissal of the head of Parkhurst Prison.
Mr Howard was asked repeatedly of Mr Lewis, "Did you threaten to overrule him?" - to which the MP repeatedly said he "did not overrule him", but ignored the "threaten" aspect of the question.
In a statement on Wednesday, Paxman said: "I have decided it is time to move on from Newsnight.
"After 25 years, I should rather like to go to bed at much the same time as most people.
"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."
The BBC said in a statement that despite deciding to leave last year, "with the appointment of a new editor and following a difficult period for Newsnight, Jeremy generously agreed to stay to help the new team bed down".
The programme was heavily criticised for not running a report which linked Jimmy Savile to allegations of child sex abuse, shortly before an ITV documentary made the allegations public.
Ofcom also upheld a complaint against an episode of Newsnight which led to Tory peer Lord McAlpine being wrongly implicated in child sex abuse allegations.
Newsnight broadcast allegations against an unnamed "leading Conservative politician from the Thatcher years" - Lord McAlpine was not named, but was the subject of internet speculation.
Ofcom criticised programme makers for not contacting Lord McAlpine prior to the broadcast, when he would have been able to inform them he had never been to the children's home in question.
Paxman started work for the BBC on Radio Brighton.
He then moved to Northern Ireland where he covered the Troubles for the BBC for three years.
He has also worked for BBC One's Tonight programme and the Six O'Clock News.