Avon was founded by European Americans along the Genesee River, across from the historic Seneca village known as Conawagus (in a transliterated spelling; also spelled as Ca-noh-wa-gas, Conewaugus, or Canawaugus, and as Ga:non'wagês in the Seneca language).

[3][page needed][4] The Seneca were among the original Five Nations of the Iroquois Confederacy and had occupied this territory for many hundreds of years prior to European encounter.

The Seneca village was located on the east side of the Genesee River, "about a mile above the ford".

[5] Ga:non'wagês was an important village to the Seneca during the eighteenth century.

European-American (white) settlers did not reach any number until about 1785, after the Americans had gained independence in the Revolutionary War and forced the Iroquois nations who had been allied with the British to cede their lands in the region.

[6] In the early 19th century, the village was noted as a spa and resort destination because of its nearby mineral springs.

The Aaron Barber Memorial Building, Avon Inn, First Methodist Episcopal Church of Avon, Hall's Opera Block, and J. Francis Kellogg House are listed on the National Register of Historic Places.

[8] According to the United States Census Bureau, the village has a total area of 3.1 square miles (8.1 km2), all land.