The decision to sell Fox’s stake in Sky rested largely with Robert A. Iger, the chief executive of Disney, who could have put pressure on Mr. Roberts had he refused to tender the shares. Comcast needs more than 50 percent of Sky’s equity to complete its offer.

Disney had aggressively pursued Sky, with Mr. Iger calling the British company a “crown jewel” of the Murdoch empire and describing its direct relationship with tens of millions of customers in Europe as a way to speed the introduction of Disney-branded streaming services. Disney also wanted to keep Sky out of the hands of one of its biggest competitors.

With the sale of the Sky stake, along with the mandated divestitures of 22 regional sports networks owned by Fox, Disney will receive roughly $30 billion to pay down debt involved with its $71.3 billion purchase of Fox and invest in its subscription streaming efforts. Disney said on Wednesday that it would “expand” its streaming plans, which include the ESPN+ sports service and a Disney-branded competitor to Netflix that will roll out next year.

The rivalry between Mr. Roberts and Mr. Iger goes back years, but it came to a head in June when Comcast topped Disney’s initial offer for the bulk of Mr. Murdoch’s empire. That forced Mr. Iger to pay about $18 billion more than he had planned in order to secure Fox’s assets. Then, on Saturday, Comcast emerged as the decisive victor in a battle with Disney for control of the British pay-television company Sky.

Disney’s agreement to sell its Sky stake raises the possibility that Comcast may be willing to make a separate deal involving the streaming service Hulu. Disney is poised to own about 60 percent of that service after it closes the deal for Fox, but Comcast would remain a minority shareholder with 30 percent. Hulu has over 20 million subscribers and is a key part of Mr. Iger’s strategy to sell Disney’s shows and films directly to consumers. Disney intends to increase spending on content at Hulu and introduce the service overseas.