Apple Inc. is betting on acclaimed director and producer Steven Spielberg for its first major foray into creating original video content.

The tech giant has struck a deal with Mr. Spielberg’s Amblin Television and Universal Television, a unit of Comcast Corp. ’s NBCUniversal, to make new episodes of “Amazing Stories,” a science fiction and horror anthology series that ran on NBC in the 1980s.

The agreement between Apple, Amblin and Universal Television calls for 10 episodes of “Amazing Stories.” Mr. Spielberg will likely be an executive producer for new the version of the show, which he created, people familiar with the matter said.

The budget for “Amazing Stories” will be significantly more than $5 million an episode, higher than most broadcast shows but on par with budgets of high-end shows on Netflix , HBO and some cable networks, according to an executive involved in the project.

“Amazing Stories” is the first show to be greenlit by Apple since it poached Sony Corp. ’s top Hollywood television executives Zack Van Amburg and Jamie Erlicht in June to help spearhead the tech company’s push into original programming.