Jellett was the son of Review Morgan Jellett (c1787-1832) and his wife Harriette Townsend, daughter of Hewitt Baldwin Poole, Esq. He was born at Cashel, County Tipperary on 25 December 1817, and educated at Kilkenny College and at Trinity College, Dublin, of which he became a fellow in 1840.
He graduated Bachelor of Arts 1838, Master of Arts
1843, Bachelor of Divinity 1866, and Doctor of Divinity 1 March 1881. He had been ordained a priest in 1846. In 1848 he was elected to the chair of natural philosophy, and in 1868 he received the appointment of commissioner of Irish national education.
In 1851 he was awarded the Cunningham Medal of the Royal Irish Academy for his work on the "Calculus of Variations".
The society later elected him their president, a position he held from 1869 to 1874. He was an able mathematician, and wrote A Treatise of the Calculus of Variations (1850), and A Treatise on the Theory of Friction (1872), as well as several papers on pure and applied mathematics, articles in the Transactions of the Royal Irish Academy, and some theological essays, sermons, and religious treatises, of which the principal were An Examination of some of the Moral Difficulties of the Old Testament (1867), and The Efficacy of Prayer (1878).
He died at the provost"s house, Trinity College, Dublin, on 19 February 1888, and was buried in Mount Jerome Cemetery on 23 February.
In 1870, on the death of Doctor Thomas Luby, he was co-opted a Senior Fellow, and thus a member of the Board of Trinity College.
