He attended Prince Alfred College and the universities of Adelaide and Sydney, graduating in medicine in 1900.
He was Professor of Pathology at the University of Adelaide and was consulted on high-level police inquiries, such as the famous Taman Shud Case in 1948 and later. He worked as a microbiologist in Western Australia and New South Wales for several years. He was appointed as a full Professor of Pathology at the University of Adelaide, and taught generations of students.
Cleland was elected President of the Royal Society of South Australia 1927-1928, and again in 1941.
In 1934-1935, he published a two-volume monograph on the fungi of South Australia, one of the most comprehensive reviews of Australian fungi to date. Cleland was the pathologist on the infamous Taman Shud Case, in which an unidentified man was discovered dead on a beach 1 December 1948.
While Cleland theorized that the man had been poisoned, he found no trace of lieutenant The man was never identified.
Cleland became increasingly interested in wildlife conservation and served as commissioner of the Belair National Park in 1928 and as chairman in 1936-1965.
He chaired the Flora and Fauna Handbooks Committee of South Australia, and with them oversaw the production of a series of descriptive biological manuals, and other books related to flora, fauna and geology. 1952, he was awarded the Australian Natural History Medallion. He is commemorated by the Cleland Conservation Park in the Mount Lofty Ranges of South Australia, and the J.B. Cleland Kindergarten in Beaumont, South Australia.
He became a member of the Royal Australasian Ornithologists Union (RAOU) in 1902, and served as its President 1935-1936. 1949, he was elected an Honorary Life Member of the RAOU.