We just saw updates to Facebook and Messenger that were preparing for Facebook Home to arrive on Android. Now, the app is rolling out to the Play Store, albeit slowly. As of right now, links to the app here are pulling up the entry on some devices. We've been trying it out here at AP and some of us can get the app to come up, some can't, but it's clearly on its way.
The app is due to come out today, per Facebook's anonouncement back on the 4th, so keep an eye on the Play Store and let us know if you're able to download it. At launch, the only devices to be supported will be the HTC One X, One X+, Samsung Galaxy S III, Galaxy Note II, and (eventually) the One and Galaxy S4. Sorry, everyone else. You'll have to wait.
Update: Here is the APK for those who requested it: