He was educated at Brasenose College, Oxford, where he matriculated in 1561. He became a fellow of Merton in 1565. He established a reputation as a Greek scholar and mathematician by voluntary lectures on the Almagest, and in 1575 became Junior Proctor. In 1578 he travelled on the continent of Europe, where he collected manuscripts and is said to have been employed by Queen Elizabeth as her resident in the Low Countries.
On his return he was named Greek Tutor to the Queen, and in 1585 was established as Warden of Merton by a vigorous exercise of the interest of Lord Burghley and Secretary Walsingham. He proved a successful and autocratic head under whom the college flourished. A translation of four Books of the Histories of Tacitus, with a learned Commentary on Roman Warfare in 1591, enhanced his reputation.
On May 26, 1596 he obtained the provostship of Eton, the reward of persistent begging. He was not qualified for the post by the statutes of the College, for he was not in orders, and the queen was reluctant to name him. Savile insisted with considerable ingenuity that the queen had a right to dispense with statutes, and at last he got his way. In February 1601 he was put under arrest on suspicion of having been concerned in the rebellion of the Earl of Essex.
He was soon released and his friendship with the faction of Essex went far to gain him the favour of James I. So no doubt did the views he had maintained in regard to the statutes of Eton. It may have been to his advantage that his elder brother, Sir John Savile (1545–1607), was a high prerogative lawyer and one of the barons of the exchequer who in 1606 affirmed the right of the king to impose import and export duties on his own authority.
On 30 September, 1604 Savile was knighted, and in that year he was named one of the body of scholars appointed to prepare the authorized version of the Bible. He was entrusted with parts of the Gospels, the Acts of the Apostles and the Book of Revelation. In 1604 died the only son born of his marriage in 1592 with Margaret Dacre, and Sir Henry Savile is thought to have been induced by this loss to devote the bulk of his fortune to the promotion of learning, though he had a daughter who survived him and who became the mother of the dramatist Sir Charles Sedley.
His edition of St. John Chrysostom in eight folio volumes was published in 1610–1613. It was printed by the king's printer in a private press erected at the expense of Sir Henry, who imported the type. The Chrysostom, which cost him £8000 and did not sell well, was the most considerable work of pure learning undertaken in England in his time. At the same press he published an edition of the Cyropaedia in 1618. In 1619 he founded and endowed his professorships of geometry and astronomy at Oxford. He died at Eton on the 19 February 1622. He is buried in Merton College Chapel where a fine mural monument offers views of contemporary Merton and Eton and references to his literary achievements (notably Chrysostom)
Sir Henry Savile has been sometimes confounded with another Henry Savile, called Long Harry (1570-1617), who gave currency to the forged addition to the Chronicle of Asser which contains the story that King Alfred founded the university of Oxford.
A brother, Thomas Savile (d. 1593), was also a member of Merton College, Oxford, and had some reputation as a scholar. His only child Elizabeth married Sir Sir John Sedley and was mother of Sir Charles Sedley.