Drummond was born at Park Place in Stirling, the son of William Drummond (d.1888) a seedsman (founder of Drummond Seeds), and his wife, Jane Campbell Blackwood (d.1910). His early education was at Stirling High School and Morrison’s Academy
Drummond was educated at Edinburgh University, where he displayed a strong inclination for physical and mathematical science. The religious element was an even more powerful factor in his nature, and disposed him to enter the Free Church of Scotland. While preparing for the ministry, he became for a time deeply interested in the evangelizing mission of Moody and Sankey, in which he actively co-operated for two years.
In 1877 he became lecturer on natural science in the Free Church College on Lynedoch Street in Glasgow, which enabled him to combine all the pursuits for which he felt a vocation. His studies resulted in his writing Natural Law in the Spiritual World, the argument of which is that the scientific principle of continuity extends from the physical world to the spiritual. Before the book was published in 1883, an invitation from the African Lakes Company drew Drummond away to Central Africa.
In 1880 he was elected a Fellow of the Royal Society of Edinburgh. His proposers were Sir Archibald Geikie, William Thomson, Lord Kelvin, John Gray McKendrick, and Sir Robert Christison.
Upon his return in the following year he found himself famous. In 1884 he was a guest at Haddo House for a dinner hosted by John Hamilton-Gordon, 1st Marquess of Aberdeen and Temair in honour of William Ewart Gladstone on his tour of Scotland. Large bodies of serious readers, among the religious and the scientific classes alike, discovered in Natural Law the common standing-ground which they needed; and the universality of the demand proved, if nothing more, the seasonableness of its publication. Drummond continued to be actively interested in missionary and other movements among the Free Church students.
In 1888 he published Tropical Africa, a valuable digest of information. In 1890 he traveled in Australia, and in 1893 delivered the Lowell Lectures at Boston. It had been his intention to reserve them for mature revision, but an attempted piracy compelled him to hasten their publication, and they appeared in 1894 under the title of The Ascent of Man. Their object was to vindicate for altruism, or the disinterested care and compassion of animals for each other, an important part in effecting the survival of the fittest, a thesis previously maintained by Professor John Fiske. In this later stage of his life he lived at 3 Park Circus in Glasgow.
Drummond’s health failed shortly afterwards (he had suffered from bone cancer for some years), and he died on 11 March 1897 whilst travelling in Tunbridge Wells. His body was returned to Holy Rude Cemetery in Stirling for burial with his parents. The grave, marked by a large distinctive red granite Celtic cross, stands just north-east of the church.
In 1905 a medallion plaque to his memory was erected in the Free Church College in Edinburgh, sculpted by James Pittendrigh Macgillivray.
Drummond never married and had no children.