Archibald Alexander was born at South River, Rockbridge County, Virginia, and raised under the tuition and ministry of Presbyterian minister william Graham (1745–1799), a man who had been trained in theology by John Witherspoon. His grandfather, of Scottish descent, came from Ireland to Pennsylvania in 1736, and after a residence of two years removed to Virginia. william, father of Archibald, was a farmer and trader. At the age of ten Archibald was sent to the academy of william Graham at Timber Ridge meetinghouse (since developed into Washington and Lee University), at Lexington. At the age of seventeen he became a tutor in the family of General John Posey, of The Wilderness, twelve miles west of Fredericksburg, but after a few months resumed his studies with his former Teacher. At this time a remarkable movement, still spoken of as "the great revival," influenced his mind and he turned his attention to the study of divinity. He was licensed to preach October 1, 1791, ordained by the presbytery of Hanover 9 June 1794, and for seven years was an itinerant pastor in Charlotte and Prince Edward counties.

His nephew, william Alexander Caruthers (1802–1846), was an American Novelist.

His eldest son, James Waddel Alexander (1804–1859) was a Princeton graduate and Presbyterian minister. He wrote the life of his father, and edited his posthumous works. His second son, william Cowper Alexander (1806–1874) served as President of the New Jersey State Senate and as the first President of the Equitable Life Assurance Society. His third son was Joseph Addison Alexander (1809–1860), a biblical scholar.

By the time he was 21 Alexander was a preacher of the Presbyterian Church. He was appointed the President of Hampden–Sydney College, where he served from 1797 to 1806 and from there he was called to the Third Presbyterian Church of Philadelphia. The Princeton Theological Seminary was established at Princeton, New Jersey in 1812 and Alexander was appointed its first professor, inaugurated on August 12, 1812. In 1824, he helped to found the Chi Phi Society along with Robert Baird and Charles Hodge. in 1843, he returned to Washington College to deliver an alumni address, which was one of his many publications.

His grandson, william C. Alexander (1848–1937), was an executive with the Equitable Life Assurance Society, author, and founder of Pi Kappa Alpha Fraternity. His great-grandson, James Waddell Alexander II (1888–1971), was a noted Mathematician and topologist.

The Presbyterian Historical Society in Philadelphia, Pennsylvania has a collection of Archibald Alexander’s personal papers dating from 1819 to 1851 including outgoing correspondence, manuscript articles and lecture notes.