In exchange, the Chiefs will trade its second-round pick in the 2013 draft, the second selection (No. 34 overall) in the round, as well as another conditional mid-round pick in 2014.
The Chiefs are expected to release former starting quarterback Matt Cassel.
Smith was the overall number one pick in 2005 and lost his starting job to Colin Kaepernick while sitting out with a concussion. Smith was injured when he played the Rams in a 24-24 tie on November 11.
The 28-year-old has thrown for 14,280 yards with 81 touchdowns and 63 interceptions in 80 career games.
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