The move adds to Disney's back catalogue high-grossing films such as the original Star Wars movies, the Marvel superhero pictures, Avatar and Deadpool, as well as TV hits such as Modern Family and The Simpsons.
It expands Disney's offerings with the FX and National Geographic cable channels, and Fox's regional sports network in the US.
The purchase also extends Disney's global reach, adding media company Star India and Fox's interests in Sky plc and Tata Sky to its portfolio.
Disney will also get majority control of the video streaming service Hulu, which is also partially owned by Comcast and Time Warner.
Disney will assume $13.7bn in Fox debt as part of the stock deal, taking the total value of the transaction to more than $66bn.