He was the eldest son of Nicholas Osborne (1620 - 18 April 1696), Clerk of the Crown of Ireland, who was seated at Cappagh, County Tyrone. The senior patrilineal grandson of Sir Richard Osborne, 2nd Baronet and wife Elizabeth Carew, Sir Thomas was heir presumptive to the baronetcy from April until October 1713 when he succeeded his cousin, the 4th baronet, in the title.
After serving as High Sheriff of County Waterford for 1672-1673, Thomas Osborne was knighted in 1679. Sir Nicholas Osborne, 6th Baronet (1686 - 13 January 1718), succeeded in the baronetcy on 10 October 1715, married in 1709 Mary Smyth (died 9 February 1762. Lady Osborne married secondly Colonel John Ramsay), daughter of the Rt Revd Thomas Smyth, Bishop of Limerick, and had two daughters:
Dorothy Osborne, married William Taylor, of Mallow and Sheriff of Cork City
Sir John Osborne Member of Parliament, 7th Baronet
Frances Osborne married John Jephson, of Carrick, Company
Tipperary
Mary Osborne, married on 22 December 1716 William Moore, Deputy Muster-Master General (died 18 March 1735)
Arabella Osborne, married in 1753 Robert Marshall, Justice of the Irish Court of Common Pleas (died 1774).
