He was the son of Edward Young, later Dean of Salisbury, and was born at his father's rectory at Upham, near Winchester, where he was baptized on 3 July 1683. He was educated at Winchester College, and matriculated in 1702 at New College, Oxford. He later moved to Corpus Christi, and in 1708 was nominated by Archbishop Tenison to a law fellowship at All Souls. He took his degree of D.C.L. in 1719.

His first publication was an Epistle to ... Lord Lansdoune (1713). It was followed by a Poem on the Last Day (1713), dedicated to Queen Anne; The Force of Religion: or Vanquished Love (1714), a poem on the execution of Lady Jane Grey and her husband, dedicated to the Countess of Salisbury; and an epistle to Joseph Addison, On the late Queen's Death and His Majesty's Accession to the Throne (1714), in which he rushed to praise the new king. The fulsome style of the dedications jars with the pious tone of the poems, and they are omitted from his own edition of his works.

About this time he came into contact with Philip, Duke of Wharton, whom he accompanied to Dublin in 1717. In 1719 his play, Busiris was produced at Drury Lane, and in 1721 his Revenge. The latter play was dedicated to Wharton, to whom it owed, said Young, its "most beautiful incident". Wharton promised him two annuities of £100 each and a sum of £600 in consideration of his expenses as a candidate for parliamentary election at Cirencester. In view of these promises Young refused two livings in the gift of All Souls' College, Oxford, and sacrificed a life annuity offered by the Marquess of Exeter if he would act as tutor to his son. Wharton failed to discharge his obligations, and Young, who pleaded his case before Lord Chancellor Hardwicke in 1740, gained the annuity but not the £600. Between 1725 and 1728 Young published a series of seven satires on The Universal Passion. They were dedicated to the Duke of Dorset, George Bubb Dodington, Sir Spencer Compton, Lady Elizabeth Germain and Sir Robert Walpole, and were collected in 1728 as Love of Fame, the Universal Passion. This is qualified by Samuel Johnson as a "very great performance," and abounds in striking and pithy couplets. Herbert Croft asserted that Young made £3000 by his satires, which compensated losses he had suffered in the South Sea Bubble. In 1726 he received, through Walpole, a pension of £200 a year. To the end of his life he continued to seek preferment, but the king regarded his pension as an adequate settlement.

In 1728 Young became a royal chaplain, and in 1730 he obtained the college living of Welwyn, Hertfordshire. In 1731 he married Lady Elizabeth Lee, daughter of the 1st Earl of Lichfield. Her daughter, by a former marriage with her cousin Francis Lee, married Henry Temple, son of the 1st Viscount Palmerston. Mrs Temple died at Lyons in 1736 on her way to Nice. Her husband and Lady Elizabeth Young died in 1740. These successive deaths are supposed to be the events referred to in the Night Thoughts as taking place "ere thrice yon moon had filled her horn."

In the preface to Night Thoughts Young states that the occasion of the poem was real, and Philander and Narcissa have been rather rashly identified with Mr and Mrs Temple. It has also been suggested that Philander represents Thomas Tickell, an old friend of Young's, who died three months after Lady Elizabeth Young. The infidel Lorenzo was thought by some to be a Sketch of Young's own son, but he was only eight years old at the time of publication. The Complaint, or Night Thoughts on Life, Death and Immortality, was published in 1742, and was followed by other "Nights," the eighth and ninth appearing in 1745. In 1753 his tragedy of The Brothers, written many years before, but suppressed because he was about to enter the Church, was produced at Drury Lane. Night Thoughts had made him famous, but he lived in almost uninterrupted retirement. He was made clerk of the closet to the Princess Dowager, Augusta of Saxe-Gotha, in 1761. He never recovered from his wife's death. He fell out with his son, who had apparently criticised the excessive influence exerted by his housekeeper Mrs Hallows. The old man refused to see his son until shortly before he died, but left him everything. A description of him is to be found in the letters of his curate and executor, John Jones, to Dr Thomas Birch (in Brit. Lib. Addit. M/s 4311). He died at Welwyn, reconciled with his spendthrift son: "he expired a little before 11 of the clock at the night of Good Friday last, the 5th instant, and was decently buried yesterday about 6 in the afternoon" (Jones to Birch).

Samuel Richardson in a letter to bookseller Andrew Millar discussed a new edition of Young’s poem, Night Thoughts (1750), which was already very popular, and which would become one of the most frequently-printed poems of the eighteenth century. Millar had purchased the copyright to the second volume of Night Thoughts (parts 7-11) from Young for £63 on 7 April 1749; the edition under discussion was the first in which Millar was involved, and it would be advertised for sale in the General Advertiser on 30 January 1750.

The young Goethe told his sister in 1766 that he was learning English from Young and Milton, and in his autobiography he confessed that Young's influence had created the atmosphere in which there was such a universal response to his seminal work The Sorrows of Young Werther. Young's name soon became a battle-cry for the young men of the Sturm und Drang movement. Young himself reinforced his reputation as a pioneer of Romanticism by precept as well as by example; in 1759, at the age of 76, he published a piece of critical prose under the title of Conjectures on Original Composition which put forward the vital doctrine of the superiority of "genius," of innate originality being more valuable than classic indoctrination or imitation, and suggested that modern Writers might dare to rival or even surpass the "ancients" of Greece and Rome … The Conjectures was a declaration of independence against the tyranny of classicism and was at once acclaimed as such becoming a milestone in the history of English, and European, literary criticism. It was immediately translated into German at Leipzig and at Hamburg and was widely and favourably reviewed. The cult of genius exactly suited the ideas of the Sturm und Drang movement and gave a new impetus to the cult of Young’ (Harold Forster, ‘Some uncollected authors XLV: Edward Young in translation I’).

William Hutchinson included a gloss on Night Thoughts in his series of lectures The Spirit of Masonry (1775), underlining the masonic symbolism of the text.

Night Thoughts was illustrated by william Blake in 1797, and by Thomas Stothard in 1799. The Poetical Works of the Rev. Edward Young ... were revised by himself for publication, and a completed edition appeared in 1778. The Complete Works, Poetry and Prose, of the Rev. Edward Young ..., with a life by John Doran, appeared in 1854. Sir Herbert Croft wrote the life included in Johnson's Lives of the Poets, but the critical remarks are by Johnson. Selections from Night Thoughts was also set by New England Congregationalist Composer william Billings in his Easter Anthem.

Young's masterpiece Night Thoughts emerged from obscurity by being mentioned in Edmund Blunden's World War One memoir, Undertones of War (1928), as a source of comfort during time in the trenches. This latter work emerged from the darkness of the more recent past thanks to its mention and discussion in Paul Fussell's The Great War and Modern Memory (1975), which discussed Blunden's reliance on Night Thoughts. Blunden's mention of Young's poem reintroduced an interesting, sometimes bombastic precursor to the early Romantics to students of English literature.

Young is said to have been a brilliant talker. Although Night Thoughts is long and disconnected, it abounds in brilliant isolated passages. Its success was enormous. It was translated into French, German, Italian, Spanish, Portuguese, Swedish, Welsh and Magyar. In France it became a classic of the romantic school. Questions as to the "sincerity" of the poet did arise in the 100 years after his death. The publication of fawning letters from Young seeking preferment led many readers to question the poet's sincerity. In a famous essay, Worldliness and Other-Worldliness, George Eliot discussed his "radical insincerity as a poetic Artist." If Young did not invent "melancholy and moonlight" in literature, he did much to spread the fashionable taste for them. Madame Klopstock thought the king ought to make him Archbishop of Canterbury, and some German critics preferred him to John Milton. Young's essay, Conjectures on Original Composition, was popular and influential on the continent, especially among Germans, as a testament advocating originality over neoclassical imitation. Young wrote good blank verse, and Samuel Johnson pronounced Night Thoughts to be one of "the few poems" in which blank verse could not be changed for rhyme but with disadvantage. The poem was a poetic treatment of sublimity and had a profound influence on the young Edmund Burke, whose philosophic investigations and writings on the Sublime and the Beautiful were a pivotal turn in 18th-century aesthetic theory.