LOS ANGELES — Robert A. Iger, Disney’s chief executive and chairman, has resigned from the board of Apple, whose growing Hollywood operation would have made it harder for him to fully engage as one of its directors.

Mr. Iger, 68, resigned on Tuesday, according to an Apple filing on Friday with the Securities and Exchange Commission. Also on Tuesday, Tim Cook, Apple’s chief executive, announced that Apple TV Plus, a subscription streaming service, will make its debut on Nov. 1 and cost $5 a month.

Apple TV Plus will offer a limited number of original television shows and films. But its arrival puts Apple in the thick of Hollywood’s so-called streaming wars. Disney owns Hulu and ESPN Plus, a sports service; Disney Plus, dedicated to all things Disney, Marvel, “Star Wars,” Pixar and National Geographic, will arrive on Nov. 12 and cost $7 a month.

Those offerings will join the subscription services Netflix, Amazon Prime and CBS All Access. WarnerMedia, owned by AT&T, will enter the fray with HBO Max next year.