The app and partnership was originally announced in June during Apple's annual developer conference.
It allows Amazon Prime members to stream a wide array of movies and TV shows, including exclusive content created by Amazon Studios such as The Grand Tour and The Man in the High Castle.
The move will appeal to Apple TV owners, who now have access to more content. It also encroaches a bit on Netflix's territory. Netflix has been available on the Apple TV for years, and now there's content from a competitor to watch.
The app doesn't appear to be promoted on the Apple TV's home screen just yet, but can be found by searching through the App Store.