(ESPN.com) - The San Francisco 49ers have agreed to trade quarterback Alex Smith to the Kansas City Chiefs, a league source confirmed to ESPN.com's John Clayton.

Kansas City 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 to acquire Smith from San Francisco, a league source told ESPN.

At this point, Smith will play under terms of his remaining contract, which calls for a guaranteed base salary of $8.5 million in 2013. There has been no discussions between the Chiefs and Smith's representatives about negotiating a new contract.

The trade can't be officially completed until March 12 when the 2013 league year begins.

The trade agreement was first reported by Fox Sports.

Smith, the 2005 No. 1 overall draft pick, lost his starting job to Colin Kaepernick while sitting out with a concussion but was professional at every turn and continued to mentor his replacement.

Before his injury, Smith had completed 26 of his last 28 passes -- including going 18-of-19 for 232 yards, three touchdowns and no interceptions in a "Monday Night Football" win at Arizona on Oct. 29.

He then sustained a concussion in the second quarter of the 49ers' next game, a 24-24 tie against St. Louis on Nov. 11. Smith sat out the next game as Kaepernick dazzled in his debut as an NFL starter, beating the Bears handily at home on "Monday Night Football." Smith didn't start again last season.

The 28-year-old quarterback has thrown for 14,280 yards with 81 touchdowns and 63 interceptions in 80 career games.

Information from ESPN.com senior writer John Clayton, ESPN NFL Insiders Adam Schefter and Ed Werder and The Associated Press was used in this report.