In other deals, the Royals traded pitcher Gaby Hernandez to the Chicago White Sox for future considerations and dealt pitcher Alex Caldera to the Washington Nationals for cash. Both are right-handers.
Whittleman, 24, has played first base and third base since he was a second-round Draft choice by the Rangers in 2005. Last season, he batted .215 with 12 homers and 53 RBIs for Class A Bakersfield and Double-A Frisco in the Rangers' organization.
Hernandez, 24, was one of the early cuts in the Royals' Major League camp this year. Last season as a starter for Triple-A Omaha, he was 10-6 with a 4.91 ERA in 31 games. He was claimed off waivers from the Boston Red Sox a year ago.
Caldera, 25, was 6-4 with a 3.25 ERA last year for Class A Wilmington and went 3-2 with a 5.12 ERA as a starter. He was a 13th-round Draft choice in 2007.