Well that didn't take long. Facebook Home has already been leaked on to the internet, with them being pulled from a HTC First device. It was meant to be officially released via the Play Store this Friday the 12th.
Modaco though has already got a copy of it. It doesn't consist of one APK however, it consists of three. Those being the main Facebook app (katana), the messenger app which integrates into your SMS (orca) and the home/launcher app (shell).
It is pre-release, so try it out at your own risk. Reports have said it's a little buggy but it mostly works. It's just a great way to find out what Facebook has in store for Android users.
Requirements for the apps is having a 1280x768 screen. You'll also need to uninstall all your current Facebook apps.
UPDATE: Even though Facebook said the tablet version wouldn't be ready, it looks like it runs nicely on the Nexus 7 after trying it out on my own one.
UPDATE 2: It looks like Facebook has just killed the party! It looks like they've switched off the ability to use Facebook Home. You can still install it, but no content will show up anymore, you'll only get blank screens.