Fox's board as recommended the deal to shareholders, saying it was "superior" to an offer from Comcast
Disney has increased its offer for the entertainment assets of 21st Century Fox.
Disney raised its offer for the assets from $52.4bn (€45.2bn) to $71.3bn (€61.5bn) and also for the first time made an alternative available to Fox shareholders who would rather receive an element of cash instead of Disney shares.
The move comes a week after Comcast, the US cable giant, offered $65bn in cash for the assets, which include 20th Century Fox - the Hollywood film studio behind hits such as Avatar, X-Men and Ice Age - US cable TV networks including FX and National Geographic and international pay television assets including Star TV in India.
The sale also includes Fox's stake in Sky plc, which owns Sky News.
This stake currently stands at 39.1% but Fox is seeking to take full control of the business prior to selling it on to Disney.
Fox's board is recommending the increased Disney offer to its shareholders and said that it was "superior" to the offer from Comcast last week.
Rupert Murdoch, executive chairman of Fox, said: "We are extremely proud of the businesses we have built at 21st Century Fox and firmly believe that this combination with Disney will unlock even more value for shareholders as the new Disney continues to set the pace at a dynamic time for our industry.
"We remain convinced that the combination of 21st Century Fox's iconic assets, brands and franchises with Disney's will create one of the greatest, most innovative companies in the world."
In February, Comcast launced a rival bid for Sky in competition with Fox and then, last week, tabled an offer for the Fox entertainment assets in competition with Disney.
The increased offer from Disney is also expected to enable Fox to raise its offer for Sky.