The former Leeds player's time with the League champions was affected by injury and he managed only 93 appearances, scoring 12 goals.
Smith, 26, will join his former Elland Road team-mates Mark Viduka and James Milner and will compete with Viduka, Obafemi Martins, Michael Owen, Albert Luque and Shola Ameobi for a striking spot at St James' Park.
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