From Diablo Wiki
On February 20, 2013 Blizzard announced a Diablo 3 console version coming to the PlayStation 3 & 4. There is no ETA or release date yet, but there will be playable demos at PAX East in March 2013, with more details to come.
The Diablo console project (not a Diablo 3 port, Blizzard insists) has been underway for a long time. Diablo 3 developers mentioned the concept all the way back in 2008 and began "exploring a Diablo-related concept for consoles" in 2010. From the start the project was headed up by Josh Mosqueira, and positions are still open.
- See dozens of Diablo 3 console news items via Diablo.IncGamers.com.
Diablo 3 Console Project Announcement
To further reiterate what’s posted on the home page: this is not an announcement of a console title. We are first and foremost developing Diablo III for Windows and Mac PCs, and we have no intention of allowing a console interpretation to delay or otherwise affect the release of the game. As always feel free to discuss this topic here, but please note that we don’t have any further details to share at this time.If you or someone you know would be interested in joining the Diablo team, then head over to the job posts to check out the requirements and submit an application.
Blizzcon 2011 Update
Jay Wilson commented on the ongoing Diablo console project from Blizzcon in October 2011. There were still no specifics, but Blizzard announced the hiring of Josh Mosqueira as the head of their console team in mid-2011, largely as a spur to hiring other qualified applicants.
[blue]We’ve hired people to work on the console. We have an internal team. We’ve spoken about it since it helps with hiring. We think Diablo 3 will work on console, we’ve experimented with controls, etc. But it’s essential to us that it not compromise the PC game at all, and it doesn’t feel like a crappy port to console either. Both should stand alone and work nicely. But we’re not announcing anything until we’re more sure about it.[/blue]
Diablo III Console Comments
Jay Wilson to Shacknews, October 2008.
- Diablo 3 director Jay Wilson also chimed in on the oft-speculated topic, noting that the game's control scheme would work rather well on consoles.
Jay Wilson to Play.tm, November 2008: 
Jay Wilson to GamingShogun, August 2009.
Christian Lichtner: We have said in the past that Diablo’s one of the games that really would translate [to consoles] well.
Past Blizzard Console Titles
Blizzard Entertainment started out small, churning out console ports for various long-forgotten games in the early 1990s. They eventually made two original console titles, The Lost Vikings and Rock and Roll Racing, before turning to larger original computer games, starting with Warcraft and Warcraft II. You can see a full listing of their early games on the Wikipedia page.
Their next console effort was Starcraft: Ghost, which was produced by independent game studios working in conjunction with Blizzard. The game lingered through several development cycles before finally going into indefinite delay in August, 2005.
Blizzard has announced no console plans since that point, though they've spoken frequently about their interest in returning to their console gaming roots, either with a port of one of their other titles or an original game, like Starcraft: Ghost.
- "...we're a company of gamers. I have two consoles at home. Sam has consoles. We're a culture of gamers. We will definitely work on a console game at some point. I have no doubt about that. It's just [a matter of] what game. What makes the most sense?"
- J. Allen Brack, production director for World of Warcraft 
As always with Blizzard, they are unlikely to announce anything until the project is well underway, but from their frequent comments on the issue it seems very likely that they've got something in the works.