Green was born at Newton Fell House, Nafferton. He worked in his father's business, which eventually expanded into constructional work. After a spell in Corbridge, Green moved to Newcastle c 1820, where he established an extensive architectural practice in the North East. Green's early works include the Literary and Philosophical Society building (1822-25). This was in the fashionable Grecian style, a very early example of which is John Stokoe's forceful Moot Hall (1810) above the Newcastle Quayside. Green's principal interest, however, lies in civil engineering projects. In 1829-31, he erected two wrought-iron suspension bridges at Scotswood (demolished 1967) and at Whorlton across the Tees. This latter still survives as the oldest bridge of its type in the country still supported, unaided, by its original chains. The Blackwell bridge in Darlington (1832) is described by Pevsner as 'an elegant road bridge in honey-coloured sandstone with three elliptical arches', with an attractive toll-house in the western approach.
On the Newcastle and North Shields railway, later to become the earliest provincial electric passenger line (1904), Green employed a system of laminated timber arches at the Ouseburn and Willington Dene. This system was widely copied for a time and Green was awarded the Institution of Civil Engineers' Telford medal for his work.