Twiss was the eldest son of the Rev. Robert Twiss. At University College, Oxford, he obtained a first-class degree in mathematics and a second in classics in 1830, and was elected a Fellow of his college, of which he was afterwards successively bursar, dean and tutor. During his connection with Oxford he was, inter alia, a public examiner in classics and mathematics, Drummond Professor of political economy (1842), and Regius Professor of Civil Law (1855). After he had forfeited his fellowship by marriage in 1862, he was elected to an honorary fellowship of University College.
He published while at Oxford an epitome of Niebuhr's History of Rome, an annotated edition of Livy and other works, but his studies mainly lay in the direction of political economy, law, chiefly international law, and international politics. In 1840, he was called to the bar at Lincoln's Inn, and became an advocate at Doctors' Commons. In the ecclesiastical courts he enjoyed a large practice, and filled many of the appointments incidental thereto, such as commissary-general of the city and diocese of Canterbury (1849), vicar-general to the archbishop (1852) and Chancellor of the diocese of London (1858). He was professor of international law at King's College London (1852–1855). In 1858, when the Probate and Divorce Acts of 1857 came into force, and the ecclesiastical jurisdiction of Doctors' Commons had died ,
Twiss, like many other leading advocates of Doctors' Commons, became a QC, and in the same year was also elected a bencher of his Inn. His successful career continued in the civil courts, and in addition to his large practice he was appointed in 1862 Advocate-General to the Admiralty, and in 1867 Queen's Advocate-General. In 1867 he was also knighted. He served during his legal career upon a great number of royal commissions, such as the Maynooth Commission in 1854, and others dealing with marriage law, neutrality, naturalization and allegiance. His reputation abroad led to his being invited in 1884 by Leopold II, king of the Belgians, to draw up the constitution of the Congo Free State.
In 1871, Twiss became involved in an unpleasant scandal, occasioned by allegations against the ante-nuptial conduct of his wife, whom he had married in 1862; and he threw up all his appointments and lived in retirement in London until his death, devoting himself to the study of international law and kindred topics. Among his more notable publications of this period were The Law of Nations in Peace and The Law of Nations in War.