 He was granted free agency on December 21, 1997 and signed with the Kansas City Royals on January 22, 1998.Rapp's 1998 season with Kansas City saw him finish 12–13, with a career high in strikeouts with 132 and an ERA of 5.30.The Royals granted Rapp free agency in December 1998 and he signed another one-year deal, this with the Boston Red Sox on January 11, 1999.