Orders for the new Apple TV will begin on 26 October, and they are expected to start shipping later the same week.
The box will cost $149 (about £100) for the 32GB model and $199 (£129) for the 64GB model. The company will continue to sell the existing box, and it may take a price cut.
The Apple TV, which plugs into a television to bring it apps, games and internet video, was revealed last month.
Mr Cook reiterated that vision of the Apple TV laying “the foundation of the future of TV” at a conference this week, where he confirmed that the release is imminent.
The new Apple TV is Apple’s fourth version of its line of set-top boxes, which was first released in 2007. But it brings a range of new features, including an App Store and a redesigned game controller, both of which are intended to bring the set-top box some of the features of a games console.
It also adds support for Siri throughout the operating system — allowing people to search for films just by asking, for instance, or see details about anything they are watching.
Apple initially said after launch that the TV would be on sale “at the end of October”. A report from 9to5mac confirmed that date, though said that it would be put on the website at the end of the month and then arrive in stores at the beginning of November.
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies