Delaware County is a county located in the US state of New York. As of the 2020 United States census, the population was 44,308. The county seat is Delhi. The county is named after the Delaware River, which was named in honor of Thomas West, 3rd Baron De La Warr, appointed governor of Virginia in 1609. The county is part of the Southern Tier r…Delaware County is a county located in the US state of New York. As of the 2020 United States census, the population was 44,308. The county seat is Delhi. The county is named after the Delaware River, which was named in honor of Thomas West, 3rd Baron De La Warr, appointed governor of Virginia in 1609. The county is part of the Southern Tier region of the state.