There hasn't been any official release for computer specs needed however what they have said in interviews is that the graphics cards they're using to test the game have to be bought off ebay they're so old, meaning the rigs they have for testing aren't top of the line stuff. They want people to be able to play without having to upgrade to something new.
I imagine you'll be just fine looking at what you have but don't quote me because I don't know what the convention rigs they have consist of and what video settings they're running. I would wager the only time you run into any issues running the game on max settings, as it seems to be with any MMO, is when you're in an area with tons of spell effects, hundreds of players and hundreds of NPCs.
Hoping they have some good coding for the larger WvWvW battles. It'd be a shame to see that part of the game fail because of overall latency issues, though I imagine I'll have my graphics turned completely down for the larger fights anyway.
As roshamjoe already explained, the minimum/recommended specs haven't been released yet. You should definitely be able to run the game fine, and the videocard is still fairly new, so I suspect max settings shouldn't be a problem. That said, we don't know yet how much of the latest features they support and what the requirements will be for using those...