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 global pay television assets including Star TV in India. Comcast, based in Philadelphia, did not immediately respond to a request for comment.
The ruling suggests regulators may have a more hard time blocking a major deal in the sector on antitrust grounds.
Fox could also rebuff Comcast's bid.
Deadline reports most analysts and industry observers had expected Disney to match Comcast, but not go so much higher.
The battle for Twenty-First Century Fox reflects a new imperative among entertainment and telecommunications firms. AT&T just bought Time Warner for $81 billion, after a federal judge rejected the government's antitrust concerns.
"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".
As of this writing, Rupert Murdoch, executive chairman of 21st Century Fox, believes that Disney is putting out the better offer, but is totally open to accepting a bid from Comcast should they raise it. The situation is fluid, and the Fox board's thinking could change, the people said. The investor vote is now scheduled for July 10. Disney originally bid $28 a share back in December.
Fox is retaining some of its assets, including Fox News and Fox Broadcasting Company, and rebranding them into a new standalone company that will be run by Murdoch and his son Lachlan.
Disney, meanwhile, could also benefit from Fox's wide range of television and film assets, which could feed into its streaming services, including a planned rival to Netflix sometimes referred to as Disneyflix.
The collar on the stock consideration will ensure that 21st Century Fox shareholders will receive a number of Disney shares equal to $38 in value if the average Disney stock price at closing is between $93.53 and $114.32.