The detonation happened shortly before 22:00 local time (20:00 GMT) in the Schwabing district and was heard across the city, local media report.
There are reports that sparks from the explosion caused the roofs of some neighbouring buildings to catch fire.
The bomb was discovered on Monday night by building workers at the site of an old bar that was being demolished.
Overnight, 2,500 residents were evacuated from the area closest to the bomb, with others living further away being told to stay in their homes.
Experts decided it was not possible to make the device safe because of its unusual fuse, which operated by means of a chemical reaction rather than the mechanical device that many Allied World War II bombs used.
The bomb was described as a highly explosive, a 550lb (250kg) device dropped by the Americans.
It is not unusual for big, unexploded bombs to be discovered in Germany, the BBC's Stephen Evans reports.
About 600 tonnes of unexploded ordnance are discovered in Germany every year.
They are usually defused safely, though in 2010 three bomb-disposal officers were killed during an attempt to make a bomb safe, our correspondent adds.
In December 2011, the biggest bomb disposal operation in Germany since 1945 was mounted in Koblenz to defuse two bombs from World War II found in the riverbed of the Rhine.
A bomb disposal team has detonated an American bomb left over from World War II found in the German city of Munich.