Answer:
Well, the invasion started after the Great Migration in 375 AD, while the Empire fell in 476 AD. Therefore, we can say that it lasted about 100 years.
Step-by-step explanation:
Roman Empire was in a bad condition, when in 375 nomadic tribes from Central Asia - Huns started the Great Migration.
Under their pressure, Germanic tribes started the invasion of the Roman Empire.
Rome was sacked in a couple of occasions, but finally fell under the attack of Ostrogoths in 476.