Arthur Clough was born in Liverpool to James Butler Clough, a cotton merchant of Welsh descent, and Anne Perfect, originally from Yorkshire. In 1822 the family moved to the United States, and Clough's childhood was spent mainly in Charleston, South Carolina. In 1828 Clough and his older brother Charles returned to England to attend school in Chester. In 1829 Clough began attending Rugby School, then under Thomas Arnold, whose strenuous views on life and education he accepted. (See Muscular Christianity.)

Cut off to a large degree from his family, he passed a somewhat solitary boyhood, devoted to the school and to early literary efforts in the Rugby Magazine. In 1836 his parents returned to Liverpool, and in 1837 he went with a scholarship to Balliol College, Oxford. Here his contemporaries included Benjamin Jowett, Arthur Penrhyn Stanley, John Campbell Shairp, William George Ward and Frederick Temple. Matthew Arnold, four years his junior, arrived the term after Clough had graduated. Clough and Arnold enjoyed an intense friendship in Oxford, but neither liked the other's poetry.

Oxford, in 1837, was in the full swirl of the High Church movement led by John Henry Newman. Clough was for a time influenced by this movement, but eventually rejected it. He surprised everyone by graduating from Oxford with only Second Class Honours, but won a fellowship with a tutorship at Oriel College. He became unwilling to teach the doctrines of the Church of England, as his tutorship required of him, and in 1848 he resigned as tutor and traveled to Paris, where he witnessed the revolution of 1848. Returning to England in a state of euphoria, he wrote his long poem The Bothie of Tober-na-Vuolich, a farewell to the academic life, following it up with poems from his time as student and tutor, in the shared publication Ambarvalia. In 1849 he witnessed another revolution, the siege of the Roman Republic, which inspired another long poem, Amours de Voyage. Easter Day, written in Naples, was a passionate denial of the Resurrection and the fore-runner of the unfinished poem Dipsychus.

Since 1846 Clough had been financially responsible for his mother and sister (following the death of his father and younger brother and the marriage of his elder brother). In the autumn of 1849, to provide for them, he became principal of University Hall, a hostel for Unitarian students at University College, London, but found its ideology as oppressive as that which he had left behind in Oxford. He soon found that he disliked London, in spite of the friendship of Thomas Carlyle and his wife Jane Welsh Carlyle. A prospect of a post in Sydney led him to engage himself to Blanche Mary Shore Smith, but when that failed to materialize, he traveled in 1852 to Cambridge, Massachusetts, encouraged by Ralph Waldo Emerson. There he remained several months, lecturing and editing an older edition of Plutarch for the booksellers, until in 1853 the offer of an examinership in the Education Office brought him to London once more. He married Shore Smith and pursued a steady official career, diversified only by an appointment in 1856 as secretary to a commission sent to study foreign military education. He devoted enormous energy to work as an unpaid secretarial assistant to his wife's cousin Florence Nightingale. He wrote virtually no poetry for six years.

In 1860 his health began to fail. He visited first Great Malvern and Freshwater, Isle of Wight. From April 1861 he traveled strenuously in Greece, Turkey and France, where he met up with the Tennyson family. Despite his fragile health, this continental tour renewed a state of euphoria like that of 1848-9, and he quickly wrote the elements of his last long poem, Mari Magno. His wife joined him on a voyage from Switzerland to Italy, where he contracted malaria. He died in Florence on 13 November. He is buried in the English Cemetery there , in a tomb that his wife and sister had Susan Horner design from Jean-François Champollion's book on Egyptian hieroglyphs. Matthew Arnold wrote the elegy of Thyrsis to his memory.

His youngest child was Blanche Athena Clough (1861—1960), who devoted her life to Newnham College, Cambridge, where her aunt (his sister) was principal.

Shortly before he left Oxford, in the stress of the Irish potato famine, Clough wrote an ethical pamphlet addressed to the undergraduates, with the title, A Consideration of Objections against the Retrenchment Association at Oxford (1847). His Homeric pastoral The Bothie of Toper-na-fuosich, afterwards renamed Tober-na-Vuolich (1848), and written in hexameter is full of socialism, reading-party humours and Scottish scenery. Ambarvalia (1849), published jointly with his friend Thomas Burbidge, contains shorter poems of various dates from circa 1840 onwards. Amours de Voyage, a novel in verse, was written at Rome in 1849; Dipsychus, a rather amorphous satire, at Venice in 1850; and the idylls which make up Mari Magno, or Tales on Board, in 1861. Amours de Voyage was republished by Persephone Books in 2009. A few lyric and elegiac pieces, later in date than the Ambarvalia, complete Clough's poetic output. His only considerable enterprise in prose was a revision of a 17th century translation of Plutarch (called the "Dryden Translation," but actually the product of translators other than Dryden) which occupied him from 1852, and was published as Plutarch's Lives (1859).

Clough's output is small and a large portion of it appeared post-humously. Anthony Kenny notes that the editions prepared by Clough's wife, Blanche, have "been criticized ... for omitting, in the interests of propriety, significant passages in Dipsychus and other poems." But editing Clough's literary remains has proven a challenging task even for later editors. Kenny goes on to state that "it was no mean feat to have placed almost all of Clough's poetry in the public domain within a decade, and to have secured for it general critical and popular acclaim."

His long poems have a certain narrative and psychological penetration, and some of his lyrics have a strength of melody to match their depth of thought. He is regarded as one of the most forward-looking English poets of the 19th century, in part due to a sexual frankness that shocked his contemporaries. He often went against the popular religious and social ideals of his day, and his verse is said to have the melancholy and the perplexity of an age of transition. His work is interesting to students of metre, owing to the experiments which he made, in the Bothie and elsewhere, with English hexameters and other types of verse formed upon classical models.