Fox News confirmed the succession plan shortly after other media reports, starting with CNBC television.
The 84-year-old tycoon will remain executive chairman of the group with his other son Lachlan as co-chairman in the move.
No timetable was given, but CNBC said the change would take place later this year or in early 2016.
The New York Times said the board would take up the transition plan next week.
The company did not immediately respond to an AFP query on the report.
James Murdoch, 42, will take over day to day management at Fox, working “in tandem with his 43-year-old brother Lachlan and his father,” according to CNBC.
Fox News, the cable channel which competes with CNN and MSNBC, will continue to be run by its president Roger Ailes, “reporting directly to Rupert Murdoch,” according to the network.
The company – which includes the Fox Hollywood studios and a range of television entities – was created two years ago when Murdoch broke off the struggling publishing operations of his News Corp. empire from the faster-growing media and entertainment operations.