He was born in Glasgow and attended Westminster School and the University of Glasgow and entered the Royal Army Medical Corps. He served in India, where he studied enteric fever and kala azar. He returned to the United Kingdom and was stationed at the Victoria Hospital in Netley in 1897. In 1900 he was made Assistant Professor of Pathology in the Army Medical School, and described a method of staining blood for malaria and other parasites -- a modification and simplification of the existing Romanowsky method using a compound of Methylene Blue and eosin, which became known as Leishman's stain.
In 1901, while examining pathologic specimens of a spleen from a patient who had died of kala azar he observed oval bodies and published his account of them in 1903. Charles Donovan of the Indian Medical Service independently found such bodies in other kala azar patients, and they are now known as Leishman-Donovan bodies, and recognized as the protozoan which causes kala azar, Leishmania donovani. Synonyms for kala azar now include leishmaniasis.