AMD's global head of technical marketing Robert Hallock confirmed to Computerbase GCN-based graphics cards will support DX12 and at least some will also support DX12 feature level 12_0. Computerbase mentions Tonga, Hawaii and the Xbox One GPU will surely support 12_0, however question marks remain for older chipsets like Bonaire, Tahiti and Pitcairn.
Meanwhile, Nvidia confirmed earlier their chipsets GM200, GM204 and GM206 will already support DX12 feature level 12_1. At GDC this year, MS gave an overview of feature level 12_0 and 12_1:
tl;dr: If you want a fully compatible DX12 card you should look into getting a Nvidia GTX 960, 970, 980, 980 Ti or Titan X. Or wait until more information regarding AMD's upcoming Fiji card(s) are released.
Meanwhile, Nvidia confirmed earlier their chipsets GM200, GM204 and GM206 will already support DX12 feature level 12_1. At GDC this year, MS gave an overview of feature level 12_0 and 12_1:
Hallock said it shouldn't be an issue that AMD cards only support feature level 12_0 since all the features relevant for games are included in 11_1 and 12_0. Also, most games will stick closely to what the consoles use and will therefore mostly use 12_0. Keep in mind, though, he's the global head of technical marketing, so his words shouldn't just be taken as gospel. Computerbase also pointed out Nvidia said the same thing when their Kepler cards didn't support feature level 11_1.
tl;dr: If you want a fully compatible DX12 card you should look into getting a Nvidia GTX 960, 970, 980, 980 Ti or Titan X. Or wait until more information regarding AMD's upcoming Fiji card(s) are released.