Just as promised, you can now officially use your Xbox One controller on PC. The drivers will be coming in a Windows update soon, but you can grab them early and get started.
They're available from the Major Nelson Blog. You can use the XBO controller with any game that's compatible with the Xbox 360 controller. As we get more PC games that appeared on Xbox One, like today's announcement of Dead Rising 3, those are likely to work natively with it as well. The blog notes connecting a USB cord as part of the process, though, so these drivers seem unlikely to work with the existing 360 wireless receiver.
An unofficial solution has been available for a few months, for those users who didn't want to wait for the Microsoft support.