William Alexander Osborne was educated in Ireland at the Upper Sullivan School, Holywood, and later at Queen's College in Belfast where he topped his final year. He then accepted an Exhibition Scholarship at the University of Tübingen, Germany, in 1851, where he studied biochemistry and physics. In 1899 he became a lecturer at University College in London, and in 1902 became assistant professor. He was known for his althleticism, his command of several languages, and for his extensive literary knowledge. In 1903 he married Ethel Elizabeth Goodson, a medical practitioner and industrial hygienist. In December 1903, he was appointed Professor of Physiology and Histology at the University of Melbourne.
From his arrival in Australia, Osborne contributed regularly to the Melbourne press. As well as his literary accomplishments, he was a frequent leader-writer for the Age (1912-13), and published a series of essays on 'The Physiology of High Altitudes' in the periodical The Trident (1908). He was also interested in dietetics, and made a large contribution to the Victorian Pure Food Act of 1905. He wrote many scientific textbooks on a variety of topics, and his Primer of Dietetics (1910) and German Grammar for Science Students (1906) were standard works which ran to several editions. He also wrote the social history, What We Owe to Ireland (1918) as well as a travel guide, The Visitor to Australia (1934), for Victoria's centenary year.
In later years Osborne lived mainly at Magnetic Island, Queensland. He was survived by his wife, son and three daughters.