James, according to two of the people, has also been pressing Lachlan to return. The brothers had become closer as a result of the hacking scandal and then their father’s divorce from Ms. Deng, which removed a significant source of tension between the father and the sons.

The family saga, which has played out in part in the pages of the British tabloids and in magazines like Vanity Fair, has long been a source of fascination to Murdoch-watchers. Elisabeth Murdoch left the company in 2000 and has established a life apart from her father’s companies, living in London with her husband, the public relations executive Matthew Freud. Though she sold her television production company, Shine, to News Corporation in a deal that valued it at $670 million in 2011, she is considered unlikely to return.

James Murdoch had shown the most willingness to succeed his father, and had successfully taken on several executive roles. But inside the company it was felt that his prospects were tarnished by the phone-hacking scandal that engulfed the company’s British newspaper division while under his leadership.

Since then he has been seeking a new direction — he was instrumental in persuading his father to sign off on buying a stake in Vice Media, for example.

Despite James Murdoch’s troubles, Rupert Murdoch has demonstrated a high degree of loyalty to him, and has even cut off ties with some former colleagues who have clashed with James. The new role suggests Rupert now believes James is ready to resume his upward trajectory in the company.

Though based in New York, where he is expected to primarily remain, James Murdoch has been increasingly visible on the studio’s Century City lot in California over the last year, Fox executives said. Indeed, Fox insiders positioned James’s new job as one that formalized a role he played for some time. He gained oversight of the Fox Networks Group, which includes the Fox broadcast network and the FX and National Geographic cable channels. (His purview notably does not include the Fox News Channel, which continues to be run by Roger Ailes.)

The move raised questions in Hollywood among those who work with and around 21st Century Fox. In a statement, Rupert Murdoch said James Murdoch would stand “alongside” Chase Carey, the chief operating officer and president. But it was not clear whether the position was an apprenticeship to Mr. Carey, or a partnership. TV agents noted that Mr. Carey’s title remained chief operating officer while James is co-chief operating officer, a subtle but potentially important distinction. Others speculated that Mr. Carey, a disciplined operator who is prized by Wall Street, might depart.