The following is from Blizzard, source here

• The character must be able to equip both items.
• Only uncommon, rare or epic items may be transmogrified. (exceptions: a select few of these items will be prevented from being used to transmogrify if they are inappropriate)
• Items must share the same armor type (examples: plate for plate, cloth for cloth)
• Weapons must be the same weapon type (exceptions: Guns, Crossbows, or Bows)
• Guns, Crossbows, and Bows can be used to transmogrify Guns, Crossbows, or Bows.
• Main hand weapons can only be used to transmogrify Main hand weapons.
• Off-hand weapons can only be used to transmogrify Off-hand weapons.
• One handed weapons can be used to transmogrify a Main hand or Off-hand weapon.
• Using an item for transmogrify makes it soulbound.
• Using an item for transmogrify makes it non-refundable.
• Using an item for transmogrify makes it non-tradable.
• Heirlooms and Account Bound items can be transmogrified.
• Heirlooms and Account Bound items can be used to transmogrify.
• Legendary items cannot be transmogrified.
• Legendary items cannot be used to transmogrify.
• Fishing Poles cannot be transmogrified.
• Fishing Poles cannot be used to transmogrify.
• Mailing an item strips its transmogrification.
• Placing an item in Void Storage strips its transmogrification.
• Vendoring an item strips its transmogrification.
• The displayed enchant will be that of the currently equipped item.
• There may be individual items that are excluded from being transmogrified on the basis that they were originally added to the game as absurdities. (examples: a weapon that looks like a fish, or a chest piece that is invisible)