Duffy, who is on the injured list with a flexor strain, waived his no-trade clause. He will be a free agent this winter.
The 32-year-old veteran had spent his entire 11-year career with the Royals, who selected him in the third round of the 2007 MLB draft.
Duffy was 4-3 with a 2.51 ERA and 65 strikeouts in 61 innings pitched for the Royals this season. He is 68-68 with a 3.95 ERA in his career.
To make room on the 40-man roster for Duffy, the Dodgers designated outfielder DJ Peters for assignment.