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.
What role will Danny Duffy have with the Dodgers?
Jeff Passan shares his thoughts on the Dodgers acquiring pitcher Danny Duffy from the Royals.