Murphy's departure had been tipped for some time, although where his exact destination would be was unclear.
Murphy helped launch BBC Three in 2003, having spent several years in roles at the BBC, including launching UK Play at the age of 26 before becoming head of programming for BBC Choice, which became BBC Three.
Speaking about his departure, Murphy hit back at comments made by MP Adam Price who asked why the channel appeared to be on a "wall-to-wall prime-time repeat loop".
"I shall not miss having to listen to some bore of an MP who can't get his facts right and doesn't watch a channel, which is not even aimed at him," Murphy said.
Jana Bennett, BBC director of television, said: "Stuart has inspired many programme makers and has been an insightful, funny, provocative and highly valued member of the BBC TV team."
BBC Three spawned the hugely popular 'Little Britain' comedy series, 'Casanova' and the medical drama 'Bodies'.
According to the BBC, the channel has now become the second most-watched digital channel with more than 9m viewers a week, beating its E4, Sky One, Living TV and Paramount.
Among those rumoured to be in line to replace Murphy include: John Keeling, the controller of UKTV Gold; Red Johnson, editor of UKTV Gold and UKTV Drama; and Richard Woolfe, director of Living TV.
BBC Three was named Best Non-Terrestrial Channel of the Year 2005 at the Media Guardian Edinburgh International Television Festival and Best General Entertainment Channel 2005 at the Broadcast Digital Channel of the Year Awards.
Murphy joins RDF as the production company is in takeover talks with IWC Media, owned by 'Newsnight' presenter Kirsty Wark and her husband, which could net the pair £3.75m. IWC Media has been valued at £15m.
His departure comes as the BBC today named Jon Beazley as the controller of entertainment commissioning across the BBC. He is currently acting controller and has been at the BBC for 20 years.
He replaces Jane Lush, one of a number of recent senior staff exits, which include head of BBC comedy Sophie Clarke-Jervoise, and Anthony Utley, BBC Worldwide director of TV distribution.
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