He was born in New York City to Scottish parents. "At the age of twelve years he made his first attempts at engraving on copper, frequently using pennies rolled out, and on type-metal plates. He received no instruction, and his knowledge was acquired by watching jewelers and other workmen." He is one of the earliest American wood-engravers. He produced works for books, periodicals, and newspapers. Anderson was a founding member of the National Academy of Design in 1826.
He was also a contemporary of Thomas Bewick, and published his first work in Arnaud Bernaud's "The Looking Glass of the Mind" in 1794.