Yes that'll be fine, but you won't get maximum settings in a few games.
I'd actually recommend going AMD for a budget like yours, and getting an FX-6300 with a decent AM3+ motherboard.
With the money you've saved, you can get yourself a better graphics card, such as a 7870.
I updated my list since i already have the 7790, that a friend will give me a lite-on optical drive and that the fx-6300 is better and cheaper !
What do you think about the performance i'll get on Battlefield 3 or Skyrim on that 1080p screen ?