He was the son of Arthur Annesley, 1st Earl of Anglesey and Elizabeth Altham.
He matriculated at Christ Church, Oxford University, on 4 December 1661.
They had children: He died intestate and the administration of his estate in England and Ireland, with a value estimated at £4,000 per annum, was granted to his widow on 6 June 1690.
He was briefly a Whig member of parliament for County Waterford in 1666, after his brother-in-law, Richard Power succeeded in his father's (Irish) peerage.
[1] On 6 April 1686 Annesley succeeded to his father's peerages of Baron Mountnorris and Earl of Anglesey, in Wales [E., 1661], Baron Annesley, of Newport Pagnel, Buckinghamshire [E., 1661] and Viscount Valentia.