The Western Roman Empire ends

Germanic general Odoacer removed the young emperor Romulus Augustulus and did not name a replacement. Historians use 476 as a convenient date for the end of Roman rule in the West, though decline was gradual.

The date is a convention. The Eastern Roman Empire continued for nearly 1,000 years.

Context

Romulus Augustulus was a teenager placed on the throne in 475 by his father, the general Orestes. In 476 Odoacer, a soldier of barbarian origin commanding the army in Italy, defeated and killed Orestes after Orestes refused demands to settle troops on Italian land. Odoacer then deposed the boy but, according to the sources, spared him and sent him into comfortable retirement.

Odoacer sent the imperial regalia to the eastern emperor Zeno in Constantinople and ruled Italy as king while nominally acknowledging Zeno. For ancient observers this was less a dramatic collapse than one more change of power in a long run of them; western emperors had by then lost Britain, Gaul, Spain and North Africa to other rulers.

Modern historians stress that 476 is a label of convenience. Some prefer to date the end to 480, when Julius Nepos, the last emperor recognized by the East, died, and many describe a slow transformation rather than a sudden fall. Odoacer himself was later overthrown by the Ostrogoth Theodoric around 493.