The 1.8-tonne British bomb was found during construction work. Defusing it is expected to take most of the day.
It will be Germany's biggest post-war evacuation for an unexploded bomb, Spiegel news reports. In 2011, 45,000 residents of Koblenz were evacuated.
On Sunday there will be little traffic, making the Augsburg job easier.
The evacuation will start at 08:00 local time (07:00 GMT) and could continue into the night, the local news website Augsburger Allgemeine says.
The operation will affect 32,000 households living within a 1.5km (0.9 mile) radius of the bomb site. Schools, sports halls and an exhibition centre will accommodate the evacuees.
Augsburg is about 80km (50 miles) north-west of Munich. It was heavily bombed during the war.
From 1942 to 1945, the Royal Air Force and US bombers carried out massive raids on German cities, often round-the-clock, designed to sap the strength of the Nazi war machine.
The authorities in Augsburg, southern Germany, plan to evacuate 54,000 people from the city centre on Christmas Day because of a World War Two bomb.