Smith is yet to make his senior bow at City, but also had first-team experience at Charlton, QPR and Dutch side FC Twente, totalling 92 games.
"Matt is a very busy and energetic midfield player but also a very good character," boss Grant McCann said.
"He loves to get on the ball and pass forward. He can play either as a number eight or a number six and suits our style of play."
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