The shift in leadership comes after last December's announcement that the Walt Disney Company plans to acquire many 21st Century Fox assets in a $52.4 billion deal, which is now pending approval - though rival media giant Comcast has threatened to derail the merger.
John Nallen, now CFO of 21st Century Fox, will serve as chief operating officer of New Fox.
Rupert will remain a co-chairman but James will leave the organization entirely once the deal is finalized to pursue other opportunities.
Comcast, the largest United States cable channel, is said to be preparing financing for a potential counterbid for the Fox operations.
Lachlan has served as executive chairman of 21st Century Fox since early 2015, when he and his younger brother James were named chairman and CEO, respectively, of their father's film and TV empire. The rest of its major Hollywood assets are in line to be sold to Disney in a $52.4 billion all-stock deal.
According to the announcement, Fox chief financial officer John Nallen will take on the role of chief operating officer as a result of the transaction.
Prior to the Disney bid Fox had made an approach to acquire the 59 per cent of Sky it did not already own, however that deal has been repeatedly held up by United Kingdom regulators over fears it would undermine media plurality.
In recent months, James has distanced himself from the politics espoused by his father and the company's flagship channel, Fox News. "The strengths of the new company, a leader in news, sports and entertainment, present truly unique opportunities".
However, Comcast is widely expected to launch its own rival bid for Fox assets this summer, which could jeopardize the Disney agreement.
Its brands will include Fox News, Fox Business and Fox Sports.
The Murdochs are expected to spearhead the new, slimmer Fox once the deal shakes out. "I look forward to joining Lachlan as we begin to establish new Fox".