Sidgwick, who was born in Oxford, came from a distinguished intellectual family; both his father and an uncle were Oxford classicists and another uncle was a professor of moral philosophy at Cambridge University. He was educated at Oxford University obtaining first class degrees in both chemistry (1895) and classics (1897). After further study in Germany, during which he obtained his PhD in 1901 from Tübingen, he returned to Oxford as a fellow and spent the remainder of his life there.

Sidgwick began his career working on organic compounds and in 1910 he produced The Organic Chemistry of Nitrogen, a classic text on the subject. In 1914 Sidgwick attended a meeting of the British Association in Australia and there he met Ernest Rutherford with whom he formed a lasting friendship. The meeting marked a turning point in his career; he became interested in atomic structure and tried to explain chemical reactions through this.

Sidgwick's theory was eventually published in 1927 in his Electronic Theory of Valency, which established his international reputation. The significance of his work was that it extended the idea of valency developed by Gilbert Lewis and Irving Langmuir to inorganic compounds, emphasizing the necessity of assuming the Bohr–Rutherford model of the atom. He introduced what he termed a coordinate bond in which, unlike the covalent bond of Lewis, both electrons are donated by one atom and accepted by the other. This explained the coordination compounds of Alfred Werner.

In his later years Sidgwick worked on his two-volume The Chemical Elements and their Compounds (1950), a massive work that attempted to demonstrate the adequacy of valency theory by showing that it applied to all compounds. The work took 25 years of Sidgwick's life and for it he was reported to have examined 10,000 scientific papers.