Smith, 28, had become expendable following the emergence of backup quarterback Colin Kaepernick, who helped lead the 49ers to the Super Bowl. San Francisco will receive a second-round draft pick in 2013 from Kansas City, and now have five picks in the first three rounds.
The trade cannot be officially finalized until Mar. 12.
Smith, who was the No. 1 overall pick in the 2005 NFL Draft, led San Francisco to a 6-2-1 record in 2012 before suffering a concussion. Kaepernick thrived in the role, sparking a quarterback controversy when Smith was activated.
Smith has made steady gains after struggling for the first half of his career with a passer rating that improved every year since 2009. In the 2011-2012 season, Smith's solid play was considered a major reason for the 49ers' appearance in the NFC Championship game to eventual-champion New York Giants. He has thrown for 2,177 yards in his seven-year career, with a passer rating of 79.1.
The addition of Smith represents another major offseason move for the Chiefs, who won just two games in 2012. In January, Kansas City hired former Philadelphia Eagles head coach Andy Reid. According to sources, quarterback Matt Cassel is expected to be waived.
Cassel has two years remaining on a $63 million, six-year deal.
The Chiefs have a history of adding former San Francisco quarterbacks. Steve DeBerg, Joe Montana, Steve Bono, and Elvis Grbac all played for both clubs.