"He's come from a massive club in Rangers and he'll fit in well here. I'm looking forward to him joining us," said manager Paul Lambert.
"He's a left-back with a terrific engine and he'll be part of a squad that will hopefully do well."
The Scot has played twice in the Champions League and five times in the Uefa Cup for Rangers.
Smith fought back from a groin problem that sidelined him for 16 months in 2006 to feature regularly in the Scottish Premier League title-winning side of 2009.
He becomes former Celtic midfielder Lambert's third close season signing after midfielder Andrew Crofts and defender Elliott Ward.
Source: BBC Sport