The app can be grabbed now from either the App Store or Google Play. A European release is expected next week on November 22.
Original story follows.
The App is set to provide second screen functionality for some PS4 titles, as well as let you access your PSN profile, check up on friends and trophies, send messages to other people who have the App or to PS4, PS3, and PS Vita users. You'll also be able to make purchases using the App and remotely download it, and also use your smartphone or tablet to turn your console on and off or as a keyboard for typing.