Richard Claverhouse Jebb was born near Dundee on 27 August 1841, eldest child of Robert Jebb, an Irish barrister (1809-1885) and Emily Harriet (1811-1883) third daughter of Heneage Horsley, dean of Brechin. His sister was the social reformer Eglantyne Louisa Jebb, (1845-1925); Eglantyne's daughters, Eglantyne and Dorothy, co-founded the Save the Children Fund. He attended St Columba's College at Rathfarnham and Charterhouse, whence he was admitted to Trinity College Cambridge on 22 February 1858 on the side of Joseph Lightfoot, later Bishop of Durham. Jebb had a sparkling undergraduate career, winning the Porson prize in 1859, the Craven Scholarship the following year and was in 1862 Senior Classic and first chancellor's medallist. In 1863 he was elected Fellow of Trinity where he helped reorganise classical teaching and introduce intercollegiate teaching in the classics. In 1869 Jebb was elected Public Orator. New Trinity statutes allowed holders of the post to marry while retaining their fellowship and Jebb took advantage of this, marrying in 1874 Caroline, (née Reynolds, 1840-1930) widow of American Civil War officer General Adam Slemmer (1828-1868).
In 1875, Jebb was elected to the chair of Greek at Glasgow, where he worked hard to win over his students, despite "Glasgow Scotch not being among his accomplishments". The affection of his charges was seen most clearly in their presentation to him on his return from serious illness.
In 1889 Benjamin Hall Kennedy died and Jebb was able to return to Cambridge to become Regius Professor of Greek, and was re-elected Fellow of Trinity. He retained both positions until his death in 1905. During this second Cambridge period Jebb was elected four times as Conservative MP for the University and was knighted in 1900, after declining the honour in 1897. He was appointed OM in 1905. Throughout his professional life he worked strenuously in the cause of ancient Greek studies. He helped found the British School at Athens and the Society for the Promotion of Hellenic Studies and was a founder member of the British Academy. He received honorary degrees from Edinburgh, Cambridge, Dublin, Bologna, and Oxford, was a fellow of London University and a corresponding member of the German Institute of Archaeology. He was elected in 1898 as professor of ancient history to the Royal Academy and in 1903 as a trustee of the British Museum. After declining it in 1897 he accepted the honour of knighthood in 1900, and in 1905 he was appointed to the Order of Merit.
Jebb published regularly. He produced elementary editions of Sophocles' Electra and Ajax in 1867 and 1868 and of Theophrastus' Characters in 1870. In 1876 he published The Attic Orators from Antiphon to Isaeus. But it is his work on Sophocles for which he is justifiably remembered. Between 1883 and 1888 he produced editions of Oedipus Tyrannus, Oedipus at Colonus and Antigone and, relocated to Cambridge, Philoctetes, Women of Trachis, Electra and Ajax between 1890 and 1896. In 1905 his edition of Bacchylides, expanding on work he had done on the British Museum papyrus was published.
He died at his home in Cambridge, Springfield on 9 December 1905, shortly after returning from a visit to South African to preside over a meeting of the educational section of the British Association. On 13 December he was buried in St. Giles's cemetery at Cambridge (now known as the Parish of the Ascension Burial Ground) after a funeral service in the chapel of Trinity College.