John Nallen, Fox's current chief financial officer, will assume a broader role as chief operating officer.
"The new Fox will begin as the only media company exclusively focused on the domestic market; focused on what Americans love best - sports, news and entertainment, built and delivered for a USA audience", Rupert Murdoch said.
Comcast, the largest USA cable channel, is said to be preparing financing for a potential counterbid for the Fox operations.
Disney would also get Fox's stake in Hulu, which is a joint venture between Disney, 21st Century Fox and Comcast, the parent company of NBC.
The deal with Disney is still a long way from being completed.
James Murdoch has been serving as the CEO of 21st Century Fox, while his brother and father have been serving as co-executive chairman. The rest of its major Hollywood assets are in line to be sold to Disney in a $52.4 billion all-stock deal.
The new Fox, which depends on approval from regulators and shareholders, will mostly be focused on U.S. news and sport broadcasting.
In recent months, James has distanced himself from the politics espoused by his father and the company's flagship channel, Fox News.
"The new Fox will begin as the only media company exclusively focused on the domestic market; focused on what Americans love best - sports, news and entertainment, built and delivered for a USA audience", said Rupert Murdoch.
The new Fox will consist of the Fox News Channel, which is the top-rated cable news channel in the country, as well as the Fox Business Network and the Fox Broadcasting Company.
"The opportunity to reshape a business strategy and an operational approach uniquely tailored to the new Fox is truly compelling", Nallen added. But that began to change after Lachlan rejoined the business almost a decade later.