Baron Annaly is a title that has been created three times, twice in the Peerage of Ireland and once in the Peerage of the United Kingdom. The first creation came in the Peerage of Ireland in 1766 when the lawyer and politician John Gore was made Baron Annaly, of Tenelick in the County of Longford. He had previously represented Jamestown and County Longford in the Irish House of Commons and served as Solicitor-General for Ireland from 1760 to 1764. Gore was the son of George Gore, younger son of Sir Arthur Gore, 1st Baronet, whose elder son Paul Gore was the grandfather of Arthur Gore, 1st Earl of Arran. George, like his son, was Attorney General and a High Court judge. Other members of the Gore family include the Gore Baronets of Magharabeg, the Barons Harlech and the Earls Temple of Stowe (a title which has come into the family through marriage). On Lord Annaly's death in 1784 the title became extinct.
The second creation came in the Peerage of Ireland in 1789 when Henry Gore was created Baron Annaly, of Tenelick, in the County of Longford. He was the younger brother of John Gore, 1st Baron Annaly of the 1766 creation. Gore had previously represented County Longford and Lanesborough in the Irish House of Commons. On his death in 1793 this title became extinct as well.