Born in New York, Anderson early became interested in copperplate engraving, an art in which he was self-taught. Breaking from this interest to study medicine, Anderson later abandoned science for his art in which he became very proficient.
In 1820 he became interested in the wood-engravings of Bewick and his followers and it was in this artform that he he is generally known as the "Father of Wood-Engraving in the United States".
Anderson is particularly known for his use of the "white-line" in wood engravings. He completed thousands of carvings and worked nearly until the end of his long life of ninety-five years. Anderson has been credited with inspiring many other artists, including Abel Bowen and George Gilbert.