Fort Amsterdam ( later called Fort James , Fort Willem Hendrick , Fort James ( again ) , Fort William , Fort Anne and Fort George between British and Dutch rule ) was a fort on the southern tip of modern-day Manhattan that was the administrative headquarters for the Dutch and then British rule of New York from 1625 to 1790 , when it was torn down after the American Revolution . Fort Amsterdam ( subsequently named Fort James , Fort Willem Hendrick , Fort James ( again ) , Fort William , Fort Anne and Fort George ) was a fort on the southern tip of Manhattan that was the administrative headquarters for the Dutch and then British rule of New York from 1625 until being torn down in 1790 after the American Revolution .