Green's father was a prosperous baker from Nottingham. Green worked for his father from the age of nine until his father's death in 1829. His father left him a mill which still stands; it has been restored and was opened to the public in 1979.

Green must have been a largely self-taught mathematician. It is known that he joined the Nottingham Subscription Library in 1823 and that the library had copies of such advanced works as the Mécanique céleste (Structure of the Heavens) of Laplace. The translator, John Toplis, was head of the local grammar school and may well have influenced Green. In 1828 Green published An Essay on the Application of Mathematics to Electricity and Magnetism. It was made available to 51 subscribers and few seem to have been aware of its appearance. The work only became widely known when Lord Kelvin came across a copy in 1845 and was so impressed that he arranged for it to be reissued in Crelle's Journal. The Essay introduced into science Green's theorem, Green's function, and the notion of the electric potential.

Following the death of his father, Green felt free to follow his scientific interests. He was encouraged in this by Sir Edward Bromhead, a local landowner, who offered to arrange Green's admission to Cambridge. At first Green was reluctant, doubting that it would be suitable “for a person of my age and Imperfect Classical attainments.” Nevertheless he arrived in Cambridge at the age of 40, finished as fourth wrangler, and was elected to a fellowship of his college in 1839. He died two years later after contracting flu, leaving seven illegitimate children.