He was born in Aberdeen, and entered King's College, Aberdeen, in 1604. About 1616 he succeeded Thomas Parker in the mastership of the free school at Southampton, an appointment which he owed to Edward Seymour, 1st Earl of Hertford. By 1622 he had been appointed, through William Laud's influence, one of Charles I's chaplains, and in that year appeared The First and Second Book of Questions and Answers upon the Book of Genesis, by Alexander Ross of Aberdeen, preacher at St. Mary's, near Southampton, and one of his Majesty's Chaplains. He was vicar of St. Mary's Church, Carisbrooke in the Isle of Wight from 1634 to his death; he left Southampton in 1642.

In Pansebeia, Ross gave a list of his books, past and to come. He died in 1654 at Bramshill House in Hampshire, where he was living with Sir Andrew Henley, and in the neighbouring Eversley church there are two tablets to his memory. Ross left many legacies, and his books were left to his friend Henley, an executor and guardian to a nephew, William Ross.

Among Ross's friends and patrons were Lewis Watson, 1st Baron Rockingham, John Tufton, 2nd Earl of Thanet, Thomas Howard, 21st Earl of Arundel, and John Evelyn. His correspondence with Henry Oxenden, in English and Latin, is in the British Museum.

He is not the Alexander Ross of the Aberdeen doctors, who remained in Scotland and died in 1639.

One of Ross's most significant accomplishments, published in the same year as the beheading of the king, was his complete translation of the Qur'an into English. Although he knew no Arabic and only poorly translated L'Alcoran de Mahomet, the 1647 French translation of Du Ryer, his translation was the first in English, and his influence faintly lingers in latter-day translations down to the present.

Richard Westfall calls him "the vigilant watchdog of conservatism and orthodoxy". He was concerned to defend Aristotle and repel the Copernican theory, as it gained ground. In 1634 he published a work on the immobility of the earth, attacking Nathanael Carpenter and Philip Landsberg. He became involved in a debate with John Wilkins and Libert Froidmond, around the beliefs of Christopher Clavius. He attacked Thomas Browne (defending, for instance, the beliefs that crystal is a sort of fossilized ice, and that garlic hinders magnetism), and many other contemporary ideas. In other controversies he took on Sir Kenelm Digby, Thomas Hobbes, and William Harvey.