Dyson's deal is worth $1.5 million, Jon Heyman of MLB Network reports.
Completion of the agreement is pending a physical, according to Mark Feinsand of MLB.com.
For Dyson, this marks a return to his original franchise. The 36-year-old was the Royals' 50th-round draft pick in 2006 and spent his first seven big-league seasons with the club. He was an important role player for the Royals' playoff teams last decade, helping them to consecutive AL pennants and the 2015 World Series title.
The Mississippi native split last season between the Pittsburgh Pirates and Chicago White Sox. After joining Chicago in a midseason trade, he mostly worked as a pinch runner and defensive replacement. In Kansas City, Dyson adds speed and outfield depth to the Royals' bench.
Dyson is a career .246/.316/.334 hitter with 21 home runs, 175 RBIs, and 256 stolen bases across parts of 11 major-league seasons with five teams.