The move was confirmed by Kelly's publicist, Leslee Dart.
Kelly's departure deprives Fox News of its second-most-watched host, behind only Bill O'Reilly.
Her contract with the network was due to run out this summer.
In the past two years, Kelly has weathered personal attacks from Donald Trump during his presidential campaign, and last summer she played a behind-the-scenes role in the ouster of Fox News founder Roger Ailes after multiple accusations of sexual harassment.
The move was first reported by The New York Times.
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