A seven-time All-Star, Chapman struggled mightily last season with the New York Yankees. He posted a 4-4 record with 9 saves, a 4.46 ERA and a 1.43 WHIP in 43 relief appearances.
Chapman's time in the Bronx appeared shaky after he was left off the team's roster for the American League Division Series against the Cleveland Guardians. The decision came after he missed a mandatory team workout.
Chapman, 34, posted a 24-14 record with 153 saves and a 2.94 ERA during his seven seasons with New York.
MLB.com first reported Chapman's agreement with the Royals.