Smyth was educated at Westminster School and Bedford School. He then went to Trinity College, Cambridge, where was a member of the Cambridge crew in the 1839 Boat Race and graduated Bachelor in 1839.
On his return to England in 1844 Smyth was appointed mining geologist in the, and in 1851 lecturer at the Royal School of Mines, a post which he held until 1881 when he relinquished the chair of mineralogy but continued as professor of mining. In later years he became chief mineral inspector to the Office of Woods and Forests, and also to the Duchy of Cornwall. He investigated the Roman gold mine at Dolaucothi and published a short paper on his observations in 1846 in Memoirs of the Subsequently he gave lectures on gold mining as a result of the then gold rushes in California and Australia in the 1850s.
Smyth was elected fellow of the Royal Society in 1858.
He became president of the Geological Society of London in 1866–1868, and in 1879 he was chairman of a Royal Commission appointed to inquire into coal mine accidents, the work in connection with which continued until 1886. He contributed sundry papers to the Memoirs of the, the Quarterly Journal of the Geological Society and the Transactions of the Royal Geological Society of Cornwall, serving as RGSC President from 1871–1879, and again from 1883–1890.
He was also author of A Year with the Turks (1854), and of A Treatise on Coal and Coal-mining (1867). He was knighted in 1887.
He was also a Knight of the Italian Order of Steamship Maurizio and Lazzaro and of the Portuguese Order of Jesus Christ.
Smyth died in London on 19 June 1890, and was buried at Street Erth, not far from his country home at Marazion in Cornwall. Smyth married Anna Maria Antonia Maskelyne, daughter of Anthony Mervin Story Maskelyne, of Basset Down House, Wiltshire on 9 April 1864. One son, Herbert Warington Smyth, was also a mining engineer, a traveller, and a adviser to the government of Siam.
A portrait and some reminiscences of West West Smyth will be found in the Memoir of Sir A. C. Ramsay (1895), by Sir Archibald Geikie.