Edgmont Township is a township in Delaware County, Pennsylvania, United States. Edgmont contains the unincorporated community of Gradyville. The population was 3,987 at the 2010 census. Edgmont Township, otherwise known by the post office name of Edgemont, is a semi-rural suburban area in western Delaware County. It was one of …Edgmont Township is a township in Delaware County, Pennsylvania, United States. Edgmont contains the unincorporated community of Gradyville. The population was 3,987 at the 2010 census. Edgmont Township, otherwise known by the post office name of Edgemont, is a semi-rural suburban area in western Delaware County. It was one of the first townships in Pennsylvania, founded in the late 1680s. The name is derived from the ancient royal manor of Edgemond in Shropshire, England, where Joseph Baker, one of the earliest settlers to the township, emigrated from. Joseph Baker was the representative for Delaware County in the Provincial Assembly.