Routt will receive $6.5 million in guarantees and will make $11 million this season as part of a three-year deal, a source said. The Raiders released him after the season from a three-year, $31.5 million deal that paid him $10 million in 2011.
"I've always had a lot of respect for Romeo Crennel with his defensive expertise, so the sky is the limit for us. When you look at that, and combine it with the pieces they have on offense, I don't see why we can't win," Routt told ESPN's Josina Anderson on Tuesday.
"I took visits with Cincinnati, Kansas City and Buffalo, and was in communication with Minnesota, Tennessee, Dallas, Houston and New Orleans. I made my decision before taking visits with those teams," Routt told ESPN.
Routt said he didn't go on any additional visits because "Kansas City seemed like the right fit."
Routt was scheduled to make $5 million had he stayed with the Raiders.
With Routt and Brandon Flowers, the Chiefs have two of the better man-to-man press corners in the AFC. Flowers signed a five-year, $52.5 million contract extension last year. With more than $71 million tied up in contracts for two cornerbacks, the Chiefs may not be able to keep Brandon Carr, who is an unrestricted free agent.
The Chiefs have paid handsomely the past couple of years in the defensive backfield. Safety Eric Berry is also signed to a $60 million, five-year deal that includes $34 million guaranteed.
Carr, 25, had a career-high four interceptions in 2011. He has started all 64 games in four seasons with the Chiefs, making 237 tackles and eight picks.
"Stanford has a proven record of success in the NFL," Crennel, who will serve as his own defensive coordinator next season. "He's a talented player that has spent seven seasons in the AFC West, so he is familiar with us and our division opponents."
The 6-1, 195-pound Routt started 30 games for the Raiders over the past two seasons. The 28-year-old cornerback is entering his eighth NFL season.
Routt's seven-year tenure in Oakland ended as the team heads in a new direction under general manager Reggie McKenzie and coach Dennis Allen.
"My first stop in the NFL was great. I don't like to look backwards," Routt told ESPN. "I think that's an old chapter. It's time to turn the page. I trust the Kansas City Chiefs to lead us in the right direction."
Routt was paid like a No. 1 cornerback but didn't deliver as such last season. He was credited with allowing eight touchdown passes last season -- tied for the second most in the NFL -- and led the league with 17 penalties committed. He did set career highs with four interceptions and 15 passes defensed, however.
NFL free agency begins March 13 but because Routt was released he was able to sign with a team before the open period for transactions begins.
Senior writer John Clayton covers the NFL for ESPN.com. Information from ESPN's Josina Anderson and The Associated Press was used in this report.