William Smith was the grandson of Joseph Smith, who had been the private secretary of British Prime Minister Pitt. He was educated at Mr. Malden's School at Brighton, UK and at Marlborough College, UK. He then went on to Trinity College, Cambridge, where he took a First Class in Classics and Theology. Smith was twice awarded the Seatonian Prize for a Sacred Poem, and his essay 'Obstacles to Missionary Success Among the Heathen' (1868) won the Maitland Prize in 1867.
Smith was ordained deacon in 1859 and became a priest in 1860. He then travelled to India, where he worked as a chaplain. When he returned to England Smith became Vicar of Trumpington, and in 1869 he was appointed Principal of St. Aidan's Theological College at Birkenhead, Merseyside. Within a year of his arrival in Australia, Smith was appointed Bishop of Sydney, and Primate of Australia and Tasmania. By 1897 he was Archbishop.
Prior to his arrival in Australia Smith published Christian Self-Denial: A Sermon in Verse (1869), Echoes of Sermons (1870) and The Brazen Serpent or The Standard of Salvation (1874). He also wrote a number of theological works. In the year of his death a collection of his manuscripts and other possessions was lost when the S. S. Waratah disappeared near the Cape of Good Hope.