What it boils down to is that Hawaii-based cards like the Radeon R9 290, 290X, and 295X2 as well as the new Tonga-based Radeon R9 285 are compatible with FreeSync. Also compatible are the Radeon R7 260X and R7 260 but other brand new cards like the Radeon R9 280, 280X, 270 and 270X won't be FreeSync compatible. Neither will be older Radeons in the HD 7000 and 8000 series because these cards don't support the latest DisplayPort standard.
A list of compatible GPUs can be found on AMD's website, this page makes a clear differentiation between GPUs that support FreeSync for video playback and power-saving purposes and GPUs that will support dynamic refresh rates during games:
All AMD Radeon™ graphics cards in the AMD Radeon™ HD 7000, HD 8000, R7 or R9 Series will support Project FreeSync for video playback and power-saving purposes. The AMD Radeon™ R9 295X2, 290X, R9 290, R7 260X and R7 260 GPUs additionally feature updated display controllers that will support dynamic refresh rates during gaming.The first FreeSync-compatible LCD displays are expected to sample this month, with retail availability slated for early 2015. NVIDIA's competing G-Sync technology has already made its way to the market via screens like the ASUS ROG Swift PG278Q and works with all Kepler-based graphics cards, going back to the GeForce GTX 600 series.
AMD APUs codenamed "Kaveri," "Kabini," "Temash," "Beema" and "Mullins" also feature the necessary hardware capabilities to enable dynamic refresh rates for video playback, gaming and power-saving purposes. All products must be connected to a display that supports DisplayPort Adaptive-Sync.