With the first expansion for Diablo III - Reaper of Souls approaching release Blizzard have detailed how The Mystic - capable of rerolling properties of your items will work.
"Have you ever looted an item whose stats were almost perfect, but one property just wasn't quite what you had hoped for? Or perhaps you found an item you love, but are starting to outgrow its power? With Enchanting, you will be able to reroll one property on a Rare or Legendary item simply by speaking to Myriam, opening up her Enchant menu, and then paying a material cost. It's that easy!
While not all properties can be rerolled, most can, and you'll be able to reroll a single property over and over again, as many times as you like. This allows Enchanting to feel meaningful, while still allowing lots of room for you to hunt for even better base items (which, of course, you can then Enchant into even more powerful items, and so on)."
For more info on the mystic - check out the blogpost.