William Thwaites was educated at the Victorian Grammar School, Collins Street, and the Model School, Spring Street. He passed the civil service examination in 1868, but continued his education at the University of Melbourne, completing a Certificate of Engineering in 1873, a Bachelor of Arts in 1873 and Master of Arts the following year.
Thwaites worked in the Victorian Public Service; in 1891, he was appointed engineer-in-chief of the Melbourne and Metropolitan Board of Works and played a major part in the design of Melbourne's sewerage system.