Routt had spent seven seasons with the Raiders, who let him go Feb. 9.
"We are excited that we were able to come to terms with Stanford," Chiefs General Manager Scott Pioli said. "He is a talented player, and as we have said in the past we are always looking to add competition at every position year-round. Stanford's experience and level of play will make him a solid addition to our defense."
Routt produced 239 tackles, 10 interceptions and two sacks in 110 games for the Raiers.
"Stanford has a proven record of success in the NFL," said Kansas City Coach Romeo Crennel, whose defense against the pass ranked sixth in the league last season but was just 12th overall. "He's a talented player that has spent seven seasons in the AFC West, so he is familiar with us and our division opponents."