The Dualshock 4 has been partially compatible with the PS3 for a while now if you just plug it in, but now it seems that you can use the controller wirelessly.
A user on Reddit posted the following steps in order to get the controller to work.
- Connect DS4 with wire to PS3 then turn on.
- Go to Accessory settings.
- Select Manage Bluetooth Devices, and scan for device.
- While scanning hold the PS & Share buttons on the DS4.
- Select Wireless Controller. The DS4 light should now be white.
- Unplug wire and test it out.
Source: Reddit