Henry Sidgwick was born in Skipton, Yorkshire in 1838, the son of the Revd William Sidgwick, headmaster of Skipton Grammar School, and Mary Crofts. He attended Rugby School, where his cousin, the future Archbishop of Canterbury, Edward White Benson was a master. Thence he entered Trinity in 1855 where he was elected to a scholarship in 1855. He gained University honours by becoming Bell Scholar in 1856 and Craven Scholar in 1857. In 1859 he was 33rd Wrangler, Senior Classic and 1st Chancellor's Medallist. He became a Fellow of Trinity in that year also.
Although Sidgwick gained a University lectureship in classics, his thoughts began to turn to philosophy, perhaps influenced by his membership of the Grote Club. At the same time he also threw himself into the cause of University and College reform, forming a powerful alliance with Henry Jackson. In the few years after the death of Whewell in 1866, the party of reform were able to achieve a number of their goals, but the religious tests on Fellowships of Trinity still remained, and Sidgwick felt duty-bound to resign his Fellowship in 1869 on grounds of conscience.
In the same year Sidgwick exchanged his lectureship in Classics for one in Moral Sciences and strove to help develop a school of philosophy in Cambridge. In 1875, Trinity appointed him Praelector in Moral and Political Philosophy and in 1885 he was elected Knightbridge Professor of Moral Philosophy and re-elected to his Trinity Fellowship. He held the chair until 1900.
Sidgwick was a strong supporter of the education of women and served at times both on the governing bodies of Newnham and Girton; his wife Eleanor (née Balfour), whom he married in 1876, was Vice-President of Newnham. He died in 1900.
Sidgwick's major publications were Methods of Ethics (1874), Principles of Political Economy (1883), and Elements of Politics (1891)