Shields posted a 3.21 ERA with 180 strikeouts and 44 walks over 227 innings in 34 starts this season. Over five postseason starts, the right-hander yielded 36 hits and 17 runs and failed to record a single out in the seventh inning.
Shields, 32, is coming off his second season in Kansas City after spending the first seven seasons of his career with the Tampa Bay Rays.
The one-time All Star (2011) has made at least 31 starts and pitched at least 200 innings in every season since his rookie year. Over nine seasons, Shields has recorded a 3.72 ERA with a 1.22 WHIP and 3.60 strikeout-to-walk ratio.
The Royals went 89-73 last season and finished in second place in the American League Central before falling to the San Francisco Giants in seven games in the World Series.