Andover was established in 1883 when the Lake Shore and Michigan Southern Railways built a line branching from Ashtabula to Youngstown. This brought work and prosperity to Andover. Railroad families, retired farmers, merchants and other business people mostly populated this area. The western part of town was settled in the rolling hills with a plentiful water supply. The eastern part of town was more level but quite swampy in some areas. This low area became part of the Pymatuning Reservoir in the 1930's. The western portion of Andover is high and rolling. The eastern part is more level and in some places quite low. It is one of the highest townships in Ashtabula County.

The first settlements were begun in the portion of the township now denominated West Andover, and for years the business of the township was conducted at this point. Epephras Lyman was the first white man to attempt the settlement in 1805 or 1806. Zadoc Steele however is the first permanent settler who brought a family into the wilderness. Originally from Connecticut, Steele selected the land that is now Andover in June 1808. One of the first settlers was Col. William Henry Morley. His son Byron Morley owned and published Andover's first newspaper "The Enterprise". He also owned first post office, drug store, general store, cheese factory, monument works and much real estate in the north side of the square. First permanent settler was Epephras Lyman. In 1805 he built a log cabin just west of what is now Stanhope-Kellogsville Rd.

The first school was taught in Andover by Miss Dorothy Houghton in the summer of 1814. This school was taught in the log barn of Francis Lyman. The first post-office was established the same year and was kept at the house of the postmaster Epephras Lyman for many years. The first orchard was planted by Zadoc Steele in about 1808 and had around one hundred trees. The first church was the Presbyterian and was established in 1818. Religious services were held in the house of Mr. Steele and the homes of other settlers.

In 1890, a major fire nearly destroyed the northeast part of. This was before a fire department even existed in Andover, but after the disaster, they purchased an old steam fire engine and wells were drilled creating Andover's first volunteer fire department.

The opera house that stood on the corner of Public Square and East Main Street was a center of the performing arts including theatre, opera and debates. President Garfield prior to his term in office was thrown down the stairs because he backed the women's suffrage movement.

The first elected officials were J.S. Morley as mayor; E.S. Hill, M.F. Covell, R.D. Bishop, E.A. Black, Hill Ward, and L.R. Griffis as councilmen; A.S. Seager as clerk; Russel Black as treasurer G.B. Hathaway and L.A. Moore as the sealers.