The Ostrogoths, like the Visigoths, were originally Indo-European. We first hear of them when they are living in Poland around 100 BC. Soon after that, some of them, along with their relatives the Visigoths, seem to have decided to migrate to the south, very gradually and slowly.
Probably bad weather at home made it impossible to feed everyone, and so some people left looking for food. Or maybe somebody else pushed them out. The Ostrogoths slowly moved south through Slovakia, and settled along the north side of the Black Sea, to the east of the Visigoths (Ostrogoths means “eastern Goths”).
The Ostrogoths took up farming and trading with the Romans and the Parthians, and lived around the Black Sea more or less peacefully for several hundred years. Ostrogothic soldiers often fought as mercenaries for the Roman army, and some Ostrogoths began to get Roman or Greek educations. In the early 300s AD, Roman missionaries converted most of the Ostrogoths to Arian Christianity. But in the 300s AD the Ostrogoths began to be pushed southward and westward by new invaders, the Huns.