William Henry Flower was born on November 30, 1831, in Stratford-upon-Avon, England.

He was an English surgeon, museum curator, and comparative anatomist. He was educated at University College, London, followed by Middlesex Hospital, where he studied medicine and surgery, graduating in 1851. After several years working in surgery, he served in the Crimean War in 1854, for which he received the Crimea Medal from Queen Victoria. Flower was appointed curator of the surgical museum of Middlesex Hospital, a post which he combined in 1858 with a lectureship in comparative anatomy. In 1857, he became a Fellow of the Royal College of Surgeons. In 1862, he became a Conservator and Professor of Comparative Anatomy at the Hunterian Museum of the Royal College of Surgeons of England, holding the post for 22 years. In 1864, he was elected a Fellow of the Royal Society. In 1882, he was awarded the Royal Medal of the Royal Society. He was also President of the Anthropological Institute (1883-1885). In 1884, he was appointed director of what were then the Natural History departments of the British Museum. In 1889, he became President of the British Association for the Advancement of Science and in 1893, President of the Museums Association.

In 1858, he married Jane Georgiana Rosetta Smyth (1835–1923). He died on July 1, 1899, in London, England.