Boyd Alexander was born on the 1 January 1873 in Cranbrook, Kent, England. He entered the 7th Battalion Rifle Brigade in 1893, attaining the rank of Captain in 1898.

At the end of the 19th century, Alexander led scientific expeditions to the Cape de Verde Islands (1897-1898) and to the Zambesi and Kafuc rivers (1898-1899) in order to study the ornithology. In 1899, he joined the Gold Coast constabulary and took part in the relief of Kumasi in 1900 (for which he received the medal and clasp). On his return to England he was offered and accepted a commission in the Rifle Brigade. In 1902, he led a scientific expedition to Fernando Po which resulted in a successful ascent of Mount St. Isabel and the discovery of many new birds.

Between 1904 and 1906, Alexander led the Alexander-Gosling Expedition which travelled across Africa from the Niger to the Nile. The expedition aimed to show that the continent could be crossed from west to east by means of its waterways. Alexander was accompanied on the expedition by Captain Claud Alexander (his brother), JoséLopes (his assistant and taxidermist), Captain G.B. Gosling, and P.A. Talbot. As a result of sickness, both Claud Alexander and Gosling died during the expedition. When Talbot returned to the west, in the middle of 1905, only Alexander and Lopes were left to finish the journey; they reached the Nile in December 1906. The following year Alexander retired from the army.

For his journey across the continent, Alexander received the Gold Medal of the Royal Geographical Society of Antwerp (1907), and the founders medal of the Royal Geographical Society of London (1908). He was also made an honorary fellow of the Royal Scottish Geographical Society (1907).

At the end of 1908, Alexander and Lopes again travelled to Africa where they visited the islands of São Thomé, Príncipe, and Annobom; the Kamerun mountain; and Lake Chad. Alexander had then intended to head for Egypt through Wadai and Darfur. However, there was much instability in the country and on reaching Nyeri (seventy miles north of Abeshr, the capital of Wadai) Alexander was murdered by natives on the 2 April 1910. Lopes, who had accompanied him since his earliest journey to the Cape Verde Islands, escaped. Alexander was buried at Maifoni, by the grave of his brother Claud. A memorial to the two brothers can be found in the Parish Church of St. Dunstan in Cranbrook, Kent, England.