Simpson was born in 1866 in Earlsferry. His was a notable golfing family, which included an elder brother, Bob Simpson, a Carnoustie-based club-maker. His cousin was the golfer, James Braid. As a boy, Simpson was the favourite caddy of Sir Alexander Grant, Principal of Edinburgh University and a regular at the course in Earlsferry, where Simpson grew up.
Hutchinson speculated that Simpson was first engaged in golf at Bembridge, before removing to Carnoustie, and then several years at the end of the 19th century at Balgownie, near Aberdeen, where he partnered with Ben Sayers. He was a professional and greenkeeper at the Royal Aberdeen Golf Club course between 1894 and 1911, during which he designed the new Murcar Links course to the north in 1909. He is credited with building at least two other golf courses at Aberdeen city's Deeside Golf Club, the Blair's Course as well as the Haughton Course. He was later a professional Royal Isle of Wight Golf Club from 1890-1891, Prestwick Golf Club from 1892-1893, and Carnoustie Golf Links in 1891-92, 1893-94 and again in 1921, after spending 10 years in Detroit, Michigan, US. In Scotland, aside from the Murcar Links course, he designed the courses at Balgownie, Nairn, and Cruden Bay (with Braid). He returned to the US in 1922, where he designed the Vincennes Country Club course in Indiana, and became a professional member there. He later moved to Tam O'Shanter in Detroit and Clovernook in Cincinnati, Ohio, as well as working in Illinois, but retired in Detroit, where he died in 1955.
- "Archibald (Archie) Simpson". The Editors of The Gazetteer for Scotland. Retrieved 5 July 2014.
- Hutchinson, Horace Gordon (1900). The Book of Golf and Golfers (Public domain ed.). Longmans, Green, and Company. p. 128.
- "Archie Simpson". Antiquegolfscotland.com. Retrieved 5 July 2014.
- "The Pioneer: Archie Simpson". Golfcoursearchitecture.net. Retrieved 5 July 2014.
- "Murcar Links Golf Club". Top100golfcourses.co.uk. Retrieved 5 July 2014.
- "Archie Simpson – Courses Built". World Golf. Retrieved 5 July 2014.
- Sieg, Terence (3 November 1997). Golf travel's guide to the world's greatest golf destinations: the ultimate resource for the discriminating golfer. Broadway Books. p. 20.
- Biography at Golfcoursearchitecture.net