He was the son of Owen Wynne (1723–1789) of Hazelwood, an MP of the Parliament of Ireland, and his wife the Hon.
He succeeded to his father's estates in 1789, inheriting Hazelwood House, Sligo.
He was elected a Member of the Irish Parliament for Sligo Borough for 1776–1790 and 1791–1800.
After the act of Union he sat as MP for Sligo in the UK Parliament in 1801–1806, resigning his seat by taking the notional crown office of profit as Escheator of Munster.
His son John Arthur Wynne (1801–1865) inherited Hazelwood, and served as MP for Sligo Borough, and his daughter Sarah married Edward Joshua Cooper of Markree Castle.