According to Wikipedia (with links adapted):
The territory of Austria, originally known as the Celtic kingdom of Noricum, was a long time ally of Rome. It was occupied rather than conquered by the Romans during the reign of Augustus and made into the province Noricum in 16 BC. Later it was conquered by a series of "barbarian" nations -- inter alia the Huns, Rugii, Lombards, Ostrogoths, Slavs, Bavarii, Avars (until c. 800), and Franks (in that order). Finally, after 48 years of Hungarian rule (907 to 955), the core territory of Austria was awarded to Leopold of Babenberg in 976 after the revolt of Henry II, Duke of Bavaria. Being part of the Holy Roman Empire the Babenbergs ruled and expanded Austria from the 10th century to the 13th century.
After Frederick II, Duke of Austria died in 1246 and left no successor, Rudolf I of Habsburg gave the lands to his sons marking the beginning of the line of the Habsburgs, who continued to govern Austria until the 20th century.
With the short exception of Charles VII Albert of Bavaria, Austrian Habsburgs held the position of German Emperor beginning in 1438 with Albert II of Habsburg until the end of the Holy Roman Empire. During the 14th and 15th century Austria continued to expand its territory until it reached the position of a European imperial power at the end of the 15th century.