He was educated at Eton and at Oriel College, Oxford. Soon afterward he entered politics and was elected Liberal M.P. for Grimsby in 1826. He was subsequently elected M.P. for Wareham in 1831, and for Halifax in December 1832.
Wood’s government career began in August 1832 when he was appointed joint secretary to the Treasury in Lord Grey’s government. Wood resigned from the post in November 1834, and became secretary to the Admiralty in April 1835. He became chancellor of the exchequer under Lord John Russell in July 1846, simultaneously becoming a member of the Privy Council; and shortly afterward, he succeeded to the baronetcy on his father’s death. Wood’s stewardship as chancellor of the exchequer, a post he held until February 1852, was not impressive. He resigned with the rest of the Russell government on 27 February 1852, but found a place in the succeeding government of Lord Aberdeen, as president of the Board of Control connected with Indian affairs. In this office he pressed forward the India Act of 1853.
On 8 February 1855 he became a member of Lord Palmerston’s cabinet as First Lord of the Admiralty, compelling Parliament to keep up the size of the navy after the conclusion of the Crimean War. Wood resigned this office in 1858. In 1859 he became secretary of state for India and spent the next few years organizing the government and finances of India in the wake of the demise of the East India Company. He eventually resigned from the Indian secretaryship, on the grounds of ill health, on 16 February 1866.
In 1865 Wood lost his parliamentary seat at Halifax but was elected for Ripon. On 21 February 1866 he was raised to the peerage as Viscount Halifax of Monk Bretton (near Barnsley, in Yorkshire), after which he gradually withdrew from active politics, although he was Lord Privy Seal from July 1870 to February 1874. He died on 8 August 1885.
He was a rather moderate Whig and was not convinced of the need to repeal the Corn Laws until 1844. He also opposed, with John Bright, the age and hours restrictions imposed on children and women by the 1844 Factory Act.
The second Earl Grey was his father-in-law, for Wood had married Mary, Grey’s fifth daughter, on 29 July 1829.