The name is first found in 1303 as "Aghastadhum". Aghe (pronounced "ave") is of similar origin as the word å, meaning stream, in this case the Avestadfors, a tributary of the Dalecarlia River. Stadhum is of similar origin as stead, or farm.
In the Scandinavian Middle Ages there was a blast furnace at the location. In 1636 the construction of a giant copper mine was initiated near the Avesta fors.
The town Avesta received partial privileges in 1641 as a town under the city of Falun, and in 1644 a copper mint was built. However, the privileges were withdrawn in 1688 due to complaints of competition from its neighbour, mainly Falun. Copper coins were continued to be minted until 1831, and the copper works was in function until 1869.
Full city rights were regranted in 1919. The designated coat of arms depict the signs for copper and iron.