“To get Disney, Marvel, Pixar and Lucasfilm to even operate on the same planet is a herculean task,” said Jeffrey A. Sonnenfeld, a dean of leadership studies at the Yale School of Management. “As media barons go, I would put Bob in a category of one.”

Now, however, just as Mr. Iger approaches what appears to be the end of his career — his new retirement date is in late 2021 — he has made an eye-popping bet that will, for better or worse, make everything he has already accomplished seem like a footnote. The 21st Century Fox acquisition is Disney’s largest, surpassing its 1995 purchase of Capital Cities/ABC for $19 billion, or roughly $31 billion after adjusting for inflation.

Mr. Iger intends to use the Fox businesses, which include the 20th Century Fox studio and a chain of 22 regional sports networks, to supercharge a plan to reposition Disney.

To a large degree, ESPN, bought as part of the Capital Cities deal, has powered Disney for two decades. But traditional television, built on third-party cable and satellite subscriptions, is now in decline as people watch more content online. Mr. Iger sees Netflix-style subscription streaming services as a new growth engine and has announced plans to rely on three of them, with each benefiting from the Fox assets. (Two of the services will be new, and one will be Hulu, which Disney would now control.)

Success is far from guaranteed.

Netflix and Amazon have a huge head start. Disney will have to learn new businesses on the fly. It will be difficult for Disney to integrate 21st Century Fox for reasons of size and culture: Fox is much rowdier. James L. Brooks, a creator of “The Simpsons,” which will move to Disney in the merger, on Thursday posted an image on Twitter “with respect.” It showed an angry Homer Simpson strangling Mickey Mouse.

While most investors and analysts cheered the merger, Doug Creutz, an analyst at Cowen and Company, wrote in a research note that Disney’s bid to compete with Netflix was “a lost cause” given that tech companies “have deep pockets and no mandate to turn an economic profit in the near term.” Other analysts praised Mr. Murdoch for exiting Hollywood while criticizing Disney for buying traditional television assets — cable channels like FX and satellite television providers like Sky.