McCleon was a starter on the Rams' Super Bowl championship team in 1999 under Vermeil.
The deal reportedly is worth more than $11 million with a signing bonus of $2 million.
"Dexter fills a position of need for us at cornerback," said Chiefs President Carl Peterson. "He will push our two starting corners and be our nickel back initially."
Eric Warfield and William Bartee are Kansas City's starting corners. McCleon will replace veteran Ray Crockett, who was waived, at nickel back, but may eventually unseat Bartee.
"He has been an outstanding starting cornerback three years for the Rams," Peterson said. "Both Dick Vermeil and our defensive backs coach Peter Giunta have a long history with Dexter and are pleased to acquire a player of his talent, as well as his experience."
McCleon, 29, spent his first six years with the Rams and started 47 of 48 games and seven postseason contests between 1999-2001. He had a career-high eight interceptions in 2000. But McCleon lost his starting job to Dre' Bly last year and played mostly at nickel back.
The Rams waived McCleon for salary cap purposes and also lost Bly, who signed a five-year, $24.5 million contract with the Detroit Lions last week.
A second-round pick in 1997, McCleon started 58 of 91 games with the Rams and had 20 interceptions and 63 passes defensed.
The addition of McCleon comes two days after the Chiefs signed free agent linebacker Shawn Barber to a seven-year, $30 million contract.
Kansas City also is pursuing free agent defensive end Hugh Douglas, a Pro Bowler each of the last three years.