Currier was born in Roxbury, Massachusetts, to Nathaniel and Hannah Currier. He attended public school until age fifteen, when he was apprenticed to the Boston printing firm of William and John Pendleton. The Pendletons were the first successful lithographers in the United States, lithography having only recently been invented in Europe, and Currier learned the process in their shop. He subsequently went to work for M. E. D. Brown in Philadelphia, in 1833. The following year, Currier moved to New York City, where he was to start a new business with John Pendleton. Pendleton backed out, and the new firm became Currier & Stodart, which lasted only one year. In addition to being a lithographer, he was also a New York City volunteer fireman in the 1850s. Nathaniel Currier is interred at Green-Wood Cemetery in Brooklyn, New York.