And in another key change disclosed by the BBC yesterday, Matthew Bannister, a high-flyer who has commercial radio experience and is also a close ally of John Birt, the Director-General, will take over as controller of Radio 1.
The choice of Mr Naughtie, 41, as joint 'A-team' anchorman with John Humphrys will be a popular one. The Aberdonian's style on The World At One has been an intelligent and measured approach to political interviews, and - despite Neil Kinnock once abandoning an interview halfway through - he is tenacious rather than hectoring.
The former Guardian political correspondent is a passionate opera fan and presents Radio 3's monthly Opera News programme. But it remains to be seen when he takes over next March whether references to Scottish Opera punctuate the breakfast programme with as much frequency and humour as references to the Halle Orchestra, Manchester United and Geoffrey Boycott punctuate Mr Redhead's sessions.
However, Mr Naughtie who described his approach as 'polite toughness' said yesterday that in the different environment of the two-and-a-half-hour morning programme he hoped that his humour, wide range of interests - including music, cricket and football - would come across. 'Today is not just about the great political and foreign story but that whole area of the way we live our lives. The great trick about the Today presenters is they cover that without sounding trite or patronising,' he said.
At Radio 1, Mr Bannister, 35, will take over from Johnny Beerling, 56, who has been controller for the last eight years. Mr Beerling, who produced the first show on Radio 1, in 1967, steps down in October.
Mr Bannister is a former deputy head of news and talks at Capital Radio, the London commercial station, where he designed and launched the popular Chris Tarrant show. He has also been managing editor of BBC Greater London Radio and most recently has worked on the BBC's programme strategy review.
His first priority will be to get the ratings back on course - at its peak, the 26-year-old station attracted 27 million listeners a week. Latest figures show these have dropped to 16 million.
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