Sadleir, youngest son of Thomas Sadleir, barrister, by his first wife, Rebecca, eldest daughter of William Woodward of Clough Prior, co. Tipperary, was born in 1774. He was educated at Trinity College, Dublin, where he became a scholar in 1794, and a fellow in 1805. He graduated B.A. 1795, M.A. 1805, B.D. and D.D. 1813. In 1816, 1817, and 1823 he was Donnellan lecturer at his college; from 1824 to 1836 Erasmus Smith Professor of Mathematics, and from 1833 to 1838 Regius Professor of Greek.
In politics he was a whig, and his advocacy of Catholic emancipation was earnest and unceasing. In conjunction with the Duke of Leinster, the archbishop of Dublin, and others, he was one of the first commissioners for administering the funds for the education of the poor in Ireland, 1831.
In 1833 he was appointed, with the primate, the lord chancellor, and other dignitaries, a commissioner to alter and amend the laws relating to the temporalities of the church of Ireland, but resigned the trust in 1837. On 22 Dec. of that year, during the viceroyalty of the Marquis of Normanby, he was made provost of Trinity College, a post which he held for fourteen years. On more than one occasion he is said to have declined a bishopric. He upheld the principle of the Queen's colleges in Ireland.
He died at Castle Knock Glebe, co. Dublin, on 14 Dec. 1851, and was buried in the vaults of Trinity College on 18 Dec. He married Letitia, daughter of Joseph Grave of Ballycommon, King's County, by whom he left five children. There is a portrait of F. Sadleir in the provost's house, Trinity College.