Broxton was 1-2 with a 5.68 ERA early this season with only 14 appearances before shutting down the rest of the season with bone spurs in his right elbow. He underwent arthroscopic surgery on the elbow on Sept. 19.
The former Los Angeles Dodgers closer is expected to set up for closer Joakim Soria.
"We are delighted to add someone as talented as Jonathan to our bullpen," Royals general manager Dayton Moore said. "He will be used in a setup role to closer Joakim Soria and will help solidify what we feel is a young and talented bullpen."