Smith, 29, spent the past seven years with the Cincinnati Bengals, playing in 82 regular-season games including 14 in 2015. The 6-foot-4, 325-pound Smith has played in every regular-season game just twice in his career.
Smith, who was a unanimous All-American at Alabama in 2008, was drafted sixth overall by the Bengals in 2009. He joins free-agent guard Alex Boone as the second new signee on the offensive line.
The Vikings had made the line a priority this offseason after quarterback Teddy Bridgewater struggled with pressure last season. They hired a new offensive line coach in Tony Sparano and re-signed right tackle Phil Loadholt, who missed last year with injury. The also picked up the fifth-year option on left tackle Matt Kalil.