Both players will sign one-year contracts, the club announced. Terms were not disclosed.
The Royals also announced they have asked waivers on catcher Paul Phillips for the purpose of giving him his outright release.
Duckworth had a 3-5 record and 4.63 ERA last season in 26 games. He began the season in the starting rotation, then made a successful shift to the bullpen before being stopped by a torn left oblique in June. Reinstated from the disabled list in September, his eight outings included a streak of 17 straight batters retired.
Smith, claimed off waivers from the Diamondbacks last July 11, batted .188 in 40 games. However, he hit six home runs in just 85 at-bats and showed his versatility by playing every infield position.
The Royals have eight players remaining eligible for salary arbitration.
Phillips was designated for assignment last Friday to clear a roster spot for Jose Guillen. He played in eight games last season for the Royals, spending most of the season with Triple-A Omaha.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.