The deal, which also includes performance bonuses, is contingent on Broxton passing a physical exam Wednesday. He will be introduced in Kansas City that day.
Royals general manager Dayton Moore said Tuesday that Broxton will be used in a setup role for closer Joakim Soria, solidifying what had been one of the big leagues' youngest bullpens.
Broxton, 27, is 25-20 with a 3.19 ERA and 84 saves over seven big league seasons. He was a National League All-Star in 2009 and 2010, but made only 14 appearances for the Dodgers last season before undergoing arthroscopic surgery on his right elbow in September.
Broxton was attractive to numerous clubs because of his willingness to sign a one-year deal and go back on the market as a free agent next winter. The Tampa Bay Rays, Texas Rangers and New York Mets all actively pursued him before he decided to sign with Kansas City.
Royals outfielder and fellow Georgia native Jeff Francoeur played an active role in recruiting Broxton, baseball sources said. Francoeur, Broxton and Kansas City manager Ned Yost recently went on a hunting trip together in Georgia. Broxton was born in Augusta and currently resides in Waynesboro.
Senior writer Jerry Crasnick covers Major League Baseball for ESPN.com. Information from The Associated Press was used in this report.