Green trained under Robert Hancock, a Worcester engraver, after which he moved to London and began working as a mezzotint engraver. He began to exhibit with the Incorporated Society of Artists from 1766, became a fellow a year later and a director in 1771. He was appointed mezzotint engraver to the king in 1773, and the following year was elected an associate engraver with the Royal Academy.Throughout the 1770s and 1780s, Green's engraving practice flourished. In the 1790s, however, several of his international speculations failed and in 1798 he was declared bankrupt. In 1805 he accepted the role of keeper of the British Institution, a post he held until his death.