Washington, who spent the past four seasons with the then-Oakland Raiders, was a teammate of Chiefs star quarterback Patrick Mahomes at Texas Tech. The 2018 NFL Most Valuable Player welcomed the tailback to Kansas City with a post on social media.
"Glad to be back with my dawg," Mahomes wrote Wednesday on Twitter. "Welcome to #ChiefsKingdom."
Washington, 27, appeared in all 16 regular-season games in 2019 and set career highs in carries (108), rushing touchdowns (three), receptions (36) and receiving yards (292).
The Raiders selected Washington in the fifth round of the 2016 NFL Draft. In 55 games in Oakland, he recorded 1,122 rushing yards and seven touchdowns on 282 carries. He also added 88 catches for 613 yards and one receiving score.