Varick is a town in Seneca County, New York, United States. The population was 1,857 at the 2010 census. The town is named after Richard Varick, an officer in the American Revolution, mayor of New York City, and uncle of the first Town Supervisor, Anthony Dey.The Town of Varick is located in the central part of the county and is southeast of Geneva, New York.There is no post office in the Town of Varick. The primary postal district covering the area is Zip Code 14541 for Romulus.