Born at the manse of Sorn, Ayrshire, on 2 June 1823, he was sixth son and eighth of the thirteen children of Rev Lewis Balfour Doctor of Divinity (1777-1860), by his wife Henrietta Scott, third daughter of George Smith, Doctor of Divinity, minister of Galston. James Balfour was a brother, Thomas Stevenson was a brother-in-law, and Robert Louis Stevenson was a nephew.
In 1845 he graduated Doctor of Medicine After acting as house surgeon to the Maternity Hospital of Edinburgh, Balfour in 1846 went to Vienna, where he studied under Joseph Škoda, Carl Ludwig Sigmund, and Wilhelm Fleischmann the homeopath.
After education at Colinton, he planned first to study veterinary science and settle in Australia. But entered the Medical School of Edinburgh. at the University of Saint Andrews, and was licensed by the Royal College of Surgeons of Edinburgh. Balfour was a general practitioner in Midlothian from 1846 till 1857, when he removed to Edinburgh, and practised as a physician on becoming Fellow of the Royal College of Physicians Edinburgh in 1861.
In 1866 he was appointed physician to the Royal Hospital for Sick Children, and from 1867 he was physician to the Royal Infirmary, being appointed consulting physician in 1882, on the expiry of his term of office.
Balfour specialised in diseases of the heart and circulation, a leading figure of his time in the area with Sir William Tennant Gairdner in Glasgow, and Charles Hilton Fagge in London. He was librarian to the College of Physicians of Edinburgh from 1873 to 1882 and from 1887 to 1899.
He received the honorary degree of Doctor of Laws at Edinburgh in 1884, and at Saint Andrews in 1896. He was appointed physician in ordinary to Queen Victoria in 1900 and honorary physician to King Edward VII in 1901.
In 1899 Balfour retired from the town centre of Edinburgh to live in Colinton, on the south-west outskirts of the city, where he died on 9 August 1903.
He is buried in the Balfour vault on the north side of Colinton church. Balfour married three times:
in 1848 to Agnes (d 1851), daughter of George Thomson, by whom he had one son, Lewis;
in 1881 to Henrietta, daughter of John Usher, who survived him.
He was president of the college 1882-1884, and was a member of the University Court of Saint Andrews for many years.
