Smith signed a three-year deal worth $18 million, including $11 million guaranteed, a source told ESPN NFL Insider Adam Schefter. His addition solidifies the cornerback spot opposite Brandon Flowers.
Smith, who was the Miami Dolphins' top cornerback, had 12 passes defensed, two interceptions and three forced fumbles last season.
The 25-year-old Smith has five interceptions and 40 passes defensed in 63 career games.
The move was made possible in part because the Chiefs cleared salary-cap space Thursday by releasing Matt Cassel. The quarterback had two years left on his six-year, $63 million contract.
"There are still a few holes left. There's no doubt about it," new Chiefs general manager John Dorsey said Wednesday when asked to assess his roster. "It's how you go and attack that. But at the end of the day, players we acquire will be able to fill all the holes we need."
Smith is the second major addition to the team's secondary this offseason. The Chiefs on Wednesday finalized a three-year contract with former Falcons cornerback Dunta Robinson, who had been released in a salary-cap move.
The 30-year-old Robinson signed with Atlanta in 2010 and became a steady figure in the secondary, known especially for his bruising hits. He had four interceptions over the past three seasons.
Schwartz, who can play guard and tackle, played in 13 games for the Vikings last season after missing the 2011 campaign with a hip problem. He started 16 games for the Panthers in 2010.
Information from The Associated Press was used in this report.