http://www.gameinformer.com/b/news/archive/2014/08/06/diablo-iii-now-allows-over-the-cloud-cross-platform-saves.aspx

In the latest console update for Blizzard's bestseller, the company has enabled the ability to transfer saves between Xbox and PlayStation platforms. You will be able to import saves from Diablo III to the Ultimate Evil Edition when it releases.

This feature works cross-platform and cross-generation. What this means is that when you insert your Ultimate Evil Edition disc, the game will automatically find your previous Diablo III save and import it.

For example, if you played Diablo III on your PS3 or 360, upon playing the Ultimate Evil Edition, you can use your previous saves on the same console. Other potential import options include PS3 to Xbox One and 360 to PS4 as well as PS3 to PS4 and 360 to Xbox One. However, 360 to PS3 (and vice-versa) and Xbox One to PS4 (and vice-versa) will not be supported. In addition, you will not be able to transfer any PC data to consoles.