The 6-foot-5, 306-pound Smith is expected to be an immediate starter for the Rams, 2-14 last season and with only five wins over the last two seasons. Terms of the contract were not disclosed.
All the team's draft picks are under contract heading into the first full-squad workout under new coach Steve Spagnuolo on Friday.
Smith began his career at Baylor as a tight end and started 31 games, 24 at left tackle and seven at right tackle, after growing out of that position. In 1,147 plays at left tackle his last two seasons, the Rams said Smith allowed only 4½ sacks.