The BBC said in a statement that Naughtie has been made a special correspondent for BBC Radio 4 and BBC News books editor.
Jamie Angus, the editor of the early Radio 4 show, said it would be "strange to contemplate" the programme without him.
He said: "Usually arriving at around 4.00am in a burst of newspapers, weapons-grade gossip – possibly involving the previous evening spent at the theatre or the opera – and always a slew of ideas of how to take that morning's programme forward, Jim was always a Today night-editor's dream.
"Out of the office and on the road, Jim was in his element. Insatiably curious and always charming, Jim has a knack of grabbing interviews in a corridor or lift you never thought you'd ever get.
"And all of it anchored by his ability as a writer for radio, second to none, always able to conjure up for the audience a sense of place – a US convention, a party conference, moving into Kosovo in a Land Rover, all of it rendered vividly for a generation of Today listeners."
Naughtie's departure will leave Today with John Humphrys, Mishal Husain, Sarah Montague and Justin Webb as presenters. Evan Davis left the Today programme for Newsnight in September last year.
The BBC press office said it had no information on if and when Naughtie will be replaced.
Naughtie, who will cover the Holyrood elections in Scotland as well as presidential elections in France and the United States in his new role, said he was "thrilled" with the move.
He said: "It was exciting to discover that the BBC and I had the same idea about what I should do next. I'm thrilled to be moving from one dream job to another, and working with the programmes across Radio 4 – including Today – that I love and have known for so long. I can't think of a more invigorating challenge. And after 21 years, I can turn off that 3am alarm at last".