Marsh is to take up a new role as editor-in-chief of the BBC's journalism training school, the BBC College of Journalism.
Marsh has been editor of the 'Today' programme since November 2002 just prior to the invasion of Iraq and was its editor as the programme became embroiled in the Hutton Report, which was sparked after the infamous two-way interview of reporter Andrew Gilligan by John Humphrys.
Stephen Mitchell, BBC head of radio news, said: "Kevin Marsh is one of the most thoughtful and innovative 'Today' editors that I have worked with over many years in BBC News. He has also been one of the most creative of editors, never settling for second best and always putting the interests of the audience first."
During his time as editor, the 'Today' programme's listening numbers have risen 160,000 since the summer and 70,000 year-on-year to 6.23m.
In his new role, March will also establish and edit the college's website and commission material to fulfil its aspiration to be a world-class online presence on journalism issues.
Marsh said he was looking to help create "a world-class college forum where all the tough issues of journalism are debated" and help maintain BBC journalism as a gold standard of international journalism.
Mark Damazar, Radio 4 controller, added: "Kevin has been an outstanding editor of Today -- the most demanding editorial job in radio journalism. He has had a huge and beneficial influence on Radio 4 for nearly 25 years -- most of the time editing some of the network's most precious programmes. It will be a very tough act to follow."
Marsh joined the BBC as a news trainee in 1978, working on 'The World at One' before later joining ITN and 'News At Ten', before coming back to the BBC as deputy editor of 'The World At One' in 1987. He has also edited 'The World at One', 'The World this Weekend' and 'PM'.
The award-winning 'Today' programme is Radio 4's flagship news and current affairs programme.
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