Technically, the PS Move controller is compatible with the PS3 fat model, but you'll need the PlayStation Eye camera to make it work. So, if you've got both of those, then you're in luck. Just don't expect the same level of motion-sensing magic you'd get on a newer console.
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It should work if the PS3 fat has gotten all of the PS3 updates. Sony says "Sony Computer Entertainment, Inc. has released the new 120 GB and 250GB PlayStation 3 systems. Functionally, there is no difference between the new PlayStation 3 models and the older models. The PlayStation 3's will still have a high-definition Blu-ray player, hard drive, Wi-Fi, and 2 USB ports. " The updates do effect the ability of the PS3 functions so if the PS3 fat has not had the updates you might want to get the latest updates for your PS3.
To connect any controller to a PS3 first plug in a USB cable to the controller. Connect this cable to the PS3 you want to connect the controller to. Press the PS button and the controller will connect.
To set up a sixaxis controller on your PS3 for the first time, plug it in with the charge cable. Then press the PS button and wait until the controller connects. Your controller will now be set up to work with your PS3.
The release date is the 18th December 2013 for PS3, PS4 and PS Vita.
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PS3 is releasing the PS3 Move without changing the Name to PS4 and the already released the PS3 with 3D capability without changing the name to PS4. They will continue to release improvements to the PS3 without changing the name as long as the older models can continue to have the new features through software updates.