According to 9to5Mac, those AirPods will appear as a new speaker option starting with tvOS 11. It should already be available in the first developer beta, and consumers will likely see it when the update arrives this fall. This means that the AirPods will automatically be set up with your Apple TV without having to manually pair it via Bluetooth. Just connect it to your phone and voila, you can start using it with your TV. Or at least that's how it's supposed to work anyway; we haven't tested it so we don't know for sure.
Apple TV (as well as Amazon's Fire TV and most other TVs these days) already supports Bluetooth audio, so you can technically use any pair of wireless headphones with it, which is great if you want to watch TV without disturbing other people in your household. If you'd rather use wired headphones instead, some Roku boxes come with remote controls that have headphone jacks. Still, if you have an Apple TV, AirPods will probably be the easiest to pair. Bonus: since you'll be wearing them at home, you won't have to worry about being seen in public.