The bomb was uncovered last week during construction work in the city's historic central district. Police say Christmas Day is the best time to defuse it because there is less traffic and it is more likely people can stay with relatives.
Police vans with loudspeakers urged procrastinators to leave ahead of a 10am deadline.
Some 32,000 homes with 54,000 residents are in the evacuation zone. Christmas morning services at the medieval cathedral with its famed boys' choir were moved.
Police aren't making any promises about how long it will take. Schools and sports facilities have been opened as shelters.
About 200 people came to the town's exhibition center and 100 to the WWK Arena sports stadium. Public transportation was free of charge for the evacuation.
Finding World War II bombs is not unusual in Germany. Much of Augsburg's historic center was destroyed on Feb. 25-26, 1944, when hundreds of British and American bombers attacked the city.