Rochester is a city in, and the county seat of, Fulton County, Indiana, United States. The population was 6,270 at the 2020 census. Roches…Rochester is a city in, and the county seat of, Fulton County, Indiana, United States. The population was 6,270 at the 2020 census. Rochester was laid out in 1835. The founder Alexander Chamberlain named it for his former hometown of Rochester, New York. The Rochester post office was established in 1836.