His son James will take over the role, while his other son Lachlan will become executive co-chairman.
Rupert Murdoch, 84, will remain as executive chairman at the company and still have the final say in matters.
The company said the matter of succession would be discussed at the next board meeting.
James Murdoch, 42, has been acting as co-chief operating officer at Fox after leaving his job running BSkyB. His new role will entail running the day-to-day business of Fox.
As executive co-chairman, Lachlan Murdoch will effectively be James’ boss.
COO Chase Carey will step down and take on a role as adviser to the company.
21st Century Fox was created two years ago after being split up from Rupert Murdoch’s less profitable media company, News Corp.
It owns the Fox Hollywood studios and television businesses.
In Q1 2015, 21st Century Fox reported net income of $975 million, while News Corp, which owns the Wall Street Journal, The Times and The Sun, made a profit of $23 million.
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