Reports of the appointment had been mentioned last week and have now been confirmed by the company in an official statement.
42-year-old James will take over as of 1 July and Rupert Murdoch, and older son Lachlan, 43, will become executive co-chairmen of Fox.
Fox said corporate functions as well as TV and film operations will now report directly to the Murdoch brothers.
Rupert said: "It has always been our priority to ensure stable, long term leadership for the company, and these appointments achieve that goal.
"Lachlan and James are each talented and accomplished executives and together, we, as shareholders and partners, will strive to take our company to new levels of growth and opportunity at a time of dynamic change in our industry."
James Murdoch has been acting as co-chief operating officer at Fox, having previously headed BSkyB, which has since changed its name to Sky.
Mr Murdoch bowed to pressure to resign as chairman of BSkyB in April 2012 in the wake of the phone-hacking scandal. He had previously been executive chairman of the Murdochs' UK newspaper group.
Rupert Murdoch - who has six children - controls 39.4% of the voting shares at Fox through the Murdoch Family Trust.
He is also chairman of News Corp, which owns the Times and Sun newspapers, as well as the Wall Street Journal and New York Post in America. News Corp and Fox demerged in June 2013.
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