The left-back spot was a problem area for City last season, and Jan Molby has been chasing Smith for months, beating off competition from First Division sides to get him.
Smith said after completing his move: "I did have other offers but after speaking to Jan Molby and hearing the plans the club have for the future it excited me and I want to be a part of it.
"Initially, the idea of dropping down to the third division did play on my mind a bit but having seen the ambitions of the club I can't see us being in it for much longer.
"The other major factor for me is that I still live in Leeds and having a club closer to home was something that I had been thinking about for a while.
"To be honest, everything has just fallen into place and I'm looking forward to the start of the season."