The minister, who came under fire earlier in the year over his relationship with Rupert Murdoch's News Corporation, has been promoted to Health Secretary.
No replacement for Hunt as Culture Secretary has been announced as yet, but he emerged from Downing Street this morning (September 4) and confirmed his new post, saying he was "incredibly honoured" by the challenge.
"It is a huge task and the biggest privilege of my life," he told the BBC.
Hunt was thought keen to remain in charge of arts, media and sport, but Cameron has opted to move him on after a successful Olympics.
In an interview with the Mail on Sunday a week ago, Hunt said that he had "learned... [his] lesson" from his handling of the Sky bid.
> Jeremy Hunt sent congratulatory text to James Murdoch
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He survived repeated calls to resign after it emerged at the Leveson Inquiry into press standards that his special advisor Adam Smith had been in extensive contact with a News Corp lobbyist.
Smith quit his post after admitting that the "volume and tone" of the email contact with Frédéric Michel had gone too far while his boss was performing a "quasi-judicial" role overseeing News Corp's proposed takeover of Sky.
It is unclear whether Hunt's departure as Culture Secretary will affect any of his major projects, including the proposed new local television networks to be launched in various cities across the UK.