The eldest of seven children, Housman was born at Valley House in Fockbury, a hamlet on the outskirts of Bromsgrove in Worcestershire, to Sarah Jane (née Williams, married 17 June 1858 in Woodchester, Gloucester) and Edward Housman (whose family came from Lancaster), and was baptised on 24 April 1859 at Christ Church, in Catshill. His mother died on his twelfth birthday, and his father, a country solicitor, remarried, to an elder cousin, Lucy, in 1873. Housman's brother Laurence Housman and their sister Clemence Housman also became Writers.

After Oxford, Jackson went to work as a clerk in the Patent Office in London and arranged a job there for Housman too. The two shared a flat with Jackson's brother Adalbert until 1885, when Housman moved to lodgings of his own, probably after Jackson responded to a declaration of love by telling Housman that he could not reciprocate his feelings. Two years later, Jackson moved to India, placing more distance between himself and Housman. When he returned briefly to England in 1889, to marry, Housman was not invited to the wedding and knew nothing about it until the couple had left the country. Adalbert Jackson died in 1892 and Housman commemorated him in a poem published as "XLII – A.J.J." of More Poems (1936).

Meanwhile, Housman pursued his classical studies independently, and published scholarly articles on such authors as Horace, Propertius, Ovid, Aeschylus, Euripides and Sophocles. He gradually acquired such a high reputation that in 1892 he was offered and accepted the professorship of Latin at University College London (UCL). When, during his tenure, an immensely rare Coverdale Bible of 1535 was discovered in the UCL library and presented to the Library Committee, Housman (who had become an atheist while still an undergraduate) remarked that it would be better to sell it to "buy some really useful books with the proceeds".

During his years in London, A. E. Housman completed A Shropshire Lad, a cycle of 63 poems. After one publisher had turned it down, he helped subsidise its publication in 1896. At first selling slowly, it rapidly became a lasting success. Its appeal to English Musicians had helped to make it widely known before World War I, when its themes struck a powerful chord with English readers. The book has been in print continuously since May 1896.

Housman's poetry, especially A Shropshire Lad, was set to music by many British, and in particular English, composers in the first half of the 20th century. The national, pastoral and traditional elements of his style resonated with similar trends in English music. In 1904 the cycle A Shropshire Lad was set by Arthur Somervell, who had begun to develop the concept of the English song-cycle in his version of Tennyson's Maud a little previously. Ralph Vaughan Williams produced his well-known settings of six songs, the cycle On Wenlock Edge, for string quartet, tenor and piano in 1909. Between 1909 and 1911 George Butterworth produced settings in two collections, Six Songs from A Shropshire Lad and Bredon Hill and Other Songs. He also wrote the orchestral tone poem A Shropshire Lad, first performed at Leeds Festival in 1912.

Although Housman's early work and his responsibilities as a professor included both Latin and Greek, he began to specialise in Latin poetry. When asked later why he had stopped writing about Greek verse, he responded, "I found that I could not attain to excellence in both." In 1911 he took the Kennedy Professorship of Latin at Trinity College, Cambridge, where he remained for the rest of his life. G. P. Goold, Classics Professor at University College, wrote of Housman's accomplishments: "The legacy of Housman's scholarship is a thing of permanent value; and that value consists less in obvious results, the establishment of general propositions about Latin and the removal of scribal mistakes, than in the shining Example he provides of a wonderful mind at work … He was and may remain the last great textual critic." Between 1903 and 1930 Housman published his critical edition of Manilius's Astronomicon in five volumes. He also edited works by Juvenal (1905) and Lucan (1926).

Ivor Gurney was another Composer who made renowned settings of Housman's poems. Towards the end of World War 1 he was working on his cycle Ludlow and Teme, for voice and string quartet (published in 1919), and went on to compose the eight-song cycle The Western Playland in 1921. One more who set Housman songs at this period was John Ireland in the song cycle, The Land of Lost Content (1920–21). Even composers not directly associated with the 'pastoral' tradition, such as Arnold Bax, Lennox Berkeley and Arthur Bliss, were attracted to Housman's poetry. A 1976 catalogue listed 400 musical settings of Housman's poems. As of 2016, Lieder Net Archive records 606 settings of 187 texts.

In the early 1920s, when Moses Jackson was dying in Canada, Housman wanted to assemble his best unpublished poems so that Jackson could read them before his death. These later poems, mostly written before 1910, show a greater variety of subject and form than those in A Shropshire Lad but lack the consistency of his previously published work. He published them as Last Poems (1922), feeling that his inspiration was exhausted and that he should not publish more in his lifetime. After his death Housman's brother, Laurence, published further poems in More Poems (1936), A. E .H.: Some Poems, Some Letters and a Personal Memoir by his Brother (1937), and Collected Poems (1939). A. E. H. includes humorous verse such as a parody of Longfellow's poem Excelsior. Housman also wrote a parodic Fragment of a Greek Tragedy, in English, published posthumously with humorous poems under the title Unkind to Unicorns.

Many colleagues were unnerved by his scathing attacks on those he thought guilty of shoddy scholarship. In his paper "The Application of Thought to Textual Criticism" (1921) Housman wrote: "A textual critic engaged upon his Business is not at all like Newton investigating the motion of the planets: he is much more like a dog hunting for fleas." He declared many of his contemporary scholars to be stupid, lazy, vain, or all three, saying: "Knowledge is good, method is good, but one thing beyond all others is necessary; and that is to have a head, not a pumpkin, on your shoulders, and brains, not pudding, in your head."

Housman was educated at King Edward's School in Birmingham and later Bromsgrove School, where he revealed his academic promise and won prizes for his poems. In 1877 he won an open scholarship to St John's College, Oxford and went there to study classics. Although introverted by nature, Housman formed strong friendships with two roommates, Moses John Jackson (1858 – January 14, 1923) and A. W. Pollard. Though Housman obtained a first in classical Moderations in 1879, his dedication to textual analysis, particularly of Propertius, led him to neglect the ancient history and philosophy that formed part of the Greats curriculum. Accordingly, he failed his Finals and had to return humiliated in Michaelmas term to resit the exam and at least gain a lower-level pass degree. Though some attribute Housman's unexpected performance in his exams directly to his unrequited feelings for Jackson, most biographers adduce more obvious causes. Housman was indifferent to philosophy and overconfident in his exceptional gifts, and he spent too much time with his friends. He may also have been distracted by news of his father's desperate illness.

In his private life Housman enjoyed gastronomy, flying in aeroplanes and making frequent visits to France, where he read "books which were banned in Britain as pornographic". But he struck A. C. Benson, a fellow don, as being "descended from a long line of maiden aunts". His feelings about his poetry were ambivalent and he certainly treated it as secondary to his scholarship. He did not speak in public about his poems until 1933, when he gave a lecture "The Name and Nature of Poetry", arguing there that poetry should appeal to emotions rather than to the intellect.

In 1942 Laurence Housman also deposited an essay entitled "A. E. Housman's 'De Amicitia'" (there is a link to the text, below in this article, under "Further reading") in the British Library, with the proviso that it was not to be published for 25 years. The essay discussed A. E. Housman's homosexuality and his love for Moses Jackson. Despite the conservative nature of the times and his own caution in public life, Housman was quite open in his poetry, and especially in A Shropshire Lad, about his deeper sympathies. Poem XXX of that sequence, for instance, speaks of how "Fear contended with desire": "Others, I am not the first, / Have willed more mischief than they durst". In More Poems, he buries his love for Moses Jackson in the very act of commemorating it, as his feelings of love are not reciprocated and must be carried unfulfilled to the grave:

Selected Prose, edited by John Carter, Cambridge University Press, 1961

From 1947, University College London's academic Common room was dedicated to his memory as the Housman Room. Blue plaques followed later elsewhere, the first being on Byron Cottage in Highgate in 1969, recording the fact that A Shropshire Lad was written there. More followed on his Worcestershire birthplace, his homes and school in Bromsgrove. The latter were encouraged by the Housman Society, which was founded in the town in 1973. Another initiative was the statue in Bromsgrove High Street, showing the poet striding with walking stick in hand. The work of local Sculptor Kenneth Potts, it was unveiled on 22 March 1985.

The blue plaques in Worcestershire were set up on the centenary of A Shropshire Lad in 1996. In September of the same year a memorial window lozenge was dedicated at Poets' Corner in Westminster Abbey The following year saw the première of Tom Stoppard's play The Invention of Love, whose subject is the relationship between Housman and Moses Jackson.

As the 150th anniversary of his birth approached, London University inaugurated its Housman lectures on classical subjects in 2005, initially given every second year then annually after 2011. The anniversary itself in 2009 saw the launch of a new edition of A Shropshire Lad, including pictures from across Shropshire taken by local Photographer Gareth Thomas. Among other events, there were performances of Vaughan Williams' On Wenlock Edge and Gurney's Ludlow and Teme at St Laurence's Church in Ludlow.