Named after Robert Fulton, the engineer famous for his steamboat.
The street was once two: Fair Street east of Broadway and Partition Street to the west. In 1816 both were named Fulton, in honour of Robert Fulton, widely credited with the first commercially successful steamboat, which in 1807 carried passengers from New York to Albany. East River ferries linked the street to Fulton Street in Brooklyn, so that, counting the ferry, it was one continuous street.