Avon was founded in 1879. The community owes its name to Avon, New York, the hometown of an early postmasters, Mr. & Mrs. George Phoenix. They operated the post office out of their home. Later, in 1900, Avon was moved 1 ½ miles northwest of the Phoenix home due to the placement of a railroad track. The City of Avon was officially incorporated in 1904. Well known residents have included George McGovern, an American historian, author, U.S. Representative, U.S. Senator, and the Democratic Party Presidential nominee in the 1972 presidential election.