Born at the manse of Sorn, Ayrshire, on 2 June 1823, he was the sixth son and eighth of the thirteen children of Rev Lewis Balfour DD (1777–1860), by his wife Henrietta Scott, third daughter of George Smith, D.D., minister of Galston; James Balfour was a brother, Thomas Stevenson was a brother-in-law, and Robert Louis Stevenson was a nephew.

After education at Colinton, he planned first to study veterinary science and settle in Australia; but entered the Medical School of Edinburgh.

[1] After acting as house surgeon to the Edinburgh Royal Maternity Hospital, Balfour in 1846 went to Vienna, where he studied under Joseph Škoda, Carl Ludwig Sigmund, and Wilhelm Fleischmann the homeopath.

[2] Balfour specialised in diseases of the heart and circulation and became a leading figure of his time in this area together with Sir William Tennant Gairdner in Glasgow, and Charles Hilton Fagge in London.

[1] In 1899 Balfour retired from the town centre of Edinburgh to live in Colinton, on the southwest outskirts of the city, where he died on 9 August 1903.

[1] In 1868, following a suggestion of his father-in-law, Dr. James Craig of Ratho, he wrote two papers on "The Treatment of Aneurysm by Iodide of Potassium".