He is being replaced by Nick Robinson, who recently took time off to recover from lung cancer.
Asked about leaving the flagship BBC Radio 4 programme, Naughtie, 64, told the Radio Times magazine: “I’m the kind of emotional guy who cries at movies.
“I’m an emotional person. I care about what I do and I’m moved by events... It’s finding the right way of saying something: if you don’t invest emotion into that, you’ll never do it. The price of investing emotion is... I will probably cry on my last day.”
Naughtie will work as a special correspondent for Radio 4 and as BBC News books editor when he leaves the show, but his literary duties will see him return to Today every Saturday morning with a regular book review slot.
He first joined the show in 1994 following the death of Brian Redhead and has interviewed US presidents and every prime minister from Margaret Thatcher onwards.
He hit the headlines five years ago when he made an embarrassing verbal slip over the name of then culture secretary Jeremy Hunt and accidentally replaced the first letter of his surname with a ‘’C’’.
Speaking about that incident, he told the magazine: “I was there with lots of bits of paper and someone was shoving headlines in front of me and I said, ‘After the news we’ll be talking to Jeremy C***’... And all I could see behind the glass were arms going up in the air, as in ‘We surrender’.
“And the guy who was passing the news bulletins to the late Rory Morrison went under the table [laughing]...”
Robinson will start on air from the autumn. Newsnight’s Laura Kuenssberg is to succeed Robinson as the BBC’s political editor.