I already have the normal copy of skyrim. I was wondering if I bought the legendary edition, would my save files carry over to it?

They should. It is the same game.

As always, make a manual back up of your saves just in case.

I did, back in the Morrowind days, get a save from the base game to load into GOTY version and the save weirded out. I reloaded it again and it was just fine. So, check your stats and character once you load the game and the save and make sure it's good. Don't worry, the weirdness is really obvious, like no skills.

I'm only asking because I bought another copy of Skyrim previously, and the save file wasn't on the game. Then again that was probably because it was from a different region. Now I'm going back to Australia where I bought the first copy, and I really want to play the DLC, but with my old characters, so I was just wondering if it would work this time.