Greensburg was established in 1886. Greensburg was named for stagecoach driver D. R. "Cannonball" Green. He once ejected Carrie Nation from his coach after she snatched a cigar from his mouth and tossed it away. In 1886, Governor John Martin organized Kiowa County and named it after the native Indians of the area. Small settlements were springing up across the plains. Donald R. Green "Cannonball Green" was instrumental in the organization of Greensburg, the town that would bear his name. Green was elected Kiowa County's first representative in the Kansas legislature in 1889.

Greensburg is home to the world's largest hand dug well. Work had begun on the well in 1887 to provide water for the steam engines of the Atchison, Topeka, Santa Fe and Pacific Railroads. When the well was completed in 1888 it was 109 feet (33 m) deep and 32 feet (9.8 m) in diameter. In 1939 it was opened as a tourist attraction allowing visitors to descend to the bottom of the well. The adjacent museum displayed a 1000-pound Pallasite Meteorite. 

Half iron and half stone, the Pallasite Meteorite (Space Wanderer) on display in the Celestial Museum at the Big Well in Greensburg, was found on the Ellis Peck farm east of Greensburg, using a device similar to a mine detector. The Space Wanderer may be old beyond imagination and from far beyond our solar system. Meteorites or "shooting stars" have awed humanity throughout history.