Deane was born at Clapham Common, England, the son of Henry Deane, a chemist and fellow of the Linnean Society of London, and his wife Jemima, née Elliott. Deane was schooled in England, matriculating in 1862, then studied at Queen's College, Galway (now the National University of Ireland, Galway), where he graduated B.A. in 1865 honours in mathematics and natural science. Like many others, he was awarded M.A. in 1882 by the Queen's University of Ireland, upon its dissolution.. Deane also studied engineering for two years and obtained his diploma at King's College London as an occasional student.