The award, named after former Kansas City Monarchs ace pitcher and outfielder Charles Wilber "Bullet" Rogan, recognizes the top pitchers in the AL and NL each season.
Greinke, 26, went 16-8 with a 2.16 ERA in 33 starts for the Royals in 2009. Included in his body of work were six complete games and three shutouts.
Carpenter, 34, posted a 17-4 mark for the Cardinals with a 2.24 ERA in 28 starts. The veteran right-hander threw three complete games and a shutout in 2009.
All of the 2009 awards will be presented in January at the Museum's 10th Annual Legacy Awards, to be held at the Convention Center in Kansas City.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.