Avon was founded across the river from the Seneca Indian village called Conawagus (or Ca-noh-wa-gas, or Conewaugus, or Canawaugus). The village was located on the west side of the Genesee River, "about a mile above the ford". The Seneca religious leader Handsome Lake was born here about 1735. Governor Blacksnake moved here shortly after his birth. Cornplanter was born here around 1750.
White settlers arrived about 1785 and formed the town in 1789 as Hartford, changed in 1808 to Avon.
Mineral springs near the village made the village locally famous as a spa in the early 19th Century. The village was incorporated in 1858. Avon was also known historically for harness racing at the Avon Driving Park.