Osborn, Missouri. Osborn is a city in Clinton and De Kalb Counties in the U.S. state of Missouri. The population was 423 at the 2010 census. The Clinton County portion of Osborn is part of the Kansas City, MO–KS Metropolitan Statistical Area, while the DeKalb County portion is part of the St. Joseph, MO–KS Metropolitan Statistical Area. The Clinton County portion of Osborn lies in Platte Township.