Routt, who spent his first seven NFL seasons with Oakland, was cut by the club on February 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."
A second-round pick of the Raiders in 2005, the Houston product has totaled 239 tackles, 10 interceptions and two sacks over 110 games.
"Stanford has a proven record of success in the NFL," Kansas City head coach Romeo Crennel said. "He's a talented player that has spent seven seasons in the AFC West, so he is familiar with us and our division opponents. We are excited to have Stanford join the team, and we are looking forward to getting started."
Routt joins a team that ranked 12th in overall defense a season ago, but placed sixth in passing defense.