Rupert Murdoch, 84, will become executive co-chairman, along with his other son Lachlan, who is currently co-chairman.
He said in a statement that his sons would “strive to take our company to new levels of growth”.
The current president, Chase Carey, will act as executive vice-president until June 2016.
Rupert Murdoch is still expected to have the final say in decisions at the company, which owns the broadcaster Fox News as well as the 20th Century Fox film studio.
It was split off from Rupert Murdoch’s less profitable newspaper business, News Corporation, two years ago.
Rupert Murdoch 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, 42, and his brother Lachlan Murdoch, 43, said in a joint statement they were both “humbled” by the opportunity to lead the company with their father and the executive team.
Chase Carey, a respected media executive, has been president and chief operating officer since 2009.
It is thought that Chase Carey’s continued presence on the board will reassure investors.
Shares in 21st Century Fox have fallen almost 13% since the start of this year, but are more than 100% higher than in June 2010.
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