This article explains that you can't technically connect your AirPods to your Xbox One, but you can still use them during a gaming session.

The official Xbox app is available for iPhone, iPad, iPod touch, and most Android smartphones and tablets. You can use it to track Xbox achievements, purchase Xbox One games, and send direct messages (DMs) to your Xbox Network friends.

Here's how to use the Xbox app and Apple AirPods together while gaming on an Xbox One console.

Pair your AirPods to your iOS or Android device.