FRANKFURT—German authorities ordered one of the country’s biggest postwar evacuations after discovering an unexploded U.S. bomb from World War II in the western city of Cologne.

Officials cleared about 20,000 people from the area surrounding Cologne’s Mülheim bridge, where the one-metric-ton bomb was found nearly 16 feet underground last week during preparations for construction work. About 800 people from fire departments, relief organizations and police were involved in the evacuation that began Wednesday morning. Hours...