Sir Martin Archer Shee was born in Dublin, the younger surviving son of Martin Shee (1719/20-1783), a merchant, and his wife, Mary (d.1771), daughter of John Archer of Dublin.
He studied drawing under Francis Robert West at the Drawing Academy of the Royal Dublin Society, and by the age of fifteen set up successfully as a portrait painter in pastel. By 1786 he was painting life-size portraits in oil and had considerable fashionable patronage. In 1788, encouraged by fellow artist Gilbert Stuart, Shee set up a practice in London. He was elected A.R.A. in 1798 and R.A. in 1780. On Lawrence's death in 1830, Shee succeeded him as President of the Royal Academy and in the same year received a knighthood.