Keiller was heir to the marmalade business of his family, James Keiller & Son that had been established in 1797 in Dundee, and exported marmalade and confectionery across the British Empire.
Keiller founded and financed the Sizaire-Berwick Motor Company.
His fourth wife, Gabrielle Keiller was also an archaeological photographer who he met in connection with Avebury.
Alexander Keiller was born at Binrock House in Dundee on 1 December 1889, the only child of businessman John Mitchell Keiller (1851-1899) and Mary Sime Greig (1862-1907), of the Dundee medical family.
When Keiller was nine, his father died, leaving him the sole heir to the wealth generated by the family's business. He was sent to Hazelwood School at Limpsfield in Surrey and from there went on to Eton College. When he was seventeen, his mother died, and he returned home to administer the family business.
On 2 June 1913, Keiller married Florence Marianne Phil-Morris (1883–1955), the daughter of artist Philip Richard Morris. They moved into Keiller's house in London. After the First World War, they were divorced.
On 29 February 1924, Keiller married Veronica Mildred Liddell (1900–1964). Veronica shared his interest in archaeology, and visited Avebury with him later that year. Following a separation, Keiller divorced Veronica in 1934.
On 16 November 1938 Keiller was married for a third time; his new wife was Doris Emerson Chapman (b. 1901), an artist. She had joined the Morven Institute of Archaeological Research, founded by Keiller, in 1937.
He later married a fourth time, to Gabrielle Style. She lived past his death in 1955, and in 1966 donated the museum and its contents to the nation.
In 1913, Keiller funded the establishment of Sizaire-Berwick, an Anglo-French manufacturer of luxury cars.
After the outbreak of the First World War, he joined the Royal Naval Volunteer Reserve as a temporary lieutenant, moving to the Royal Naval Air Service in December 1914. In 1915 he was invalided out of the service, but in 1918 he joined air intelligence, where he remained until the end of the war.
Keiller began to pursue an interest in archaeology. In 1922 he and O. G. S. Crawford undertook an aerial survey of archaeological sites in south western England. This work led to their publication of Wessex from the Air in 1928, the first book of aerial archaeology to be published in the UK.
Using his wealth, Keiller decided to buy nearby Windmill Hill and then undertake excavations there. His work proved that the site was a causewayed enclosure, and it became the monument type-site for decades afterward. In 1934, he began a two-year excavation of the West Kennet Avenue, which led south east from the Avebury stone circle. As he discovered buried stones, he had them re-erected, and marked the stone-holes with pillars.
Keiller's first major excavation at Avebury was in 1937, the first of three seasons over the ensuing years. Each concentrated on a quadrant of the circle, clearing undergrowth, restoring and conserving the site. Buried stones, some up to a metre below ground, were uncovered and replaced in their original stone-holes. As with the avenue, he placed concrete pylons to denote missing stones. That same year, he founded the Morven Institute of Archaeological Research.
In 1938 he discovered the famous barber surgeon of Avebury skeleton in the south west quadrant. Keiller opened his museum that year, to display finds from the Windmill Hill, West Kennet, and Avebury excavations.
Keiller leased and restored Avebury Manor & Garden, now a National Trust property consisting of an early 16th-century manor house and its surrounding garden.
The Second World War ended excavations at Avebury. Keiller joined the special constabulary at Marlborough and as his duties left little time for archaeology, he had the museum mothballed.
In 1943, Keiller sold his holdings in Avebury to the National Trust for £12,000, simply the agricultural value of the 950 acres (3.8 km2) he had accrued. This did not reflect the immense investment he had made at the site. In 1966, his widow Gabrielle Keiller donated the Avebury museum and its contents to the nation.
In 1986, UNESCO designated Avebury (together with Stonehenge and associated sites) as a World Heritage Site. In 2000, it received over 350,000 visitors.