According to their official press release, Sentai Filmworks
has licensed Persona 4 The Animation
Sentai Filmworks will be distributing the series digitally with a DVD and Blu-ray release in 2012.
Source: Sentai Press Release
Update on September 29th
Persona 4 The Animation will be available for free on The Anime Network weekly starting October 6th, the same day that it airs in Japan.
Source: The Anime Network Press Release