The family of media mogul Rupert Murdoch has reached a deal on control of the 94-year-old's empire after his death, ensuring no change in editorial direction at Fox News, the most popular network for US President Donald Trump.

The arrangement, announced by News Corp and Fox Corp on Monday, will see Murdoch's eldest son Lachlan Murdoch shore up control of the family media empire which includes Fox News and the Wall Street Journal.