George Alfred Brown was born in 1914 in a Peabody Trust housing estate in Lambeth, the fourth son of George Brown, a grocer's packer and lorry driver. He passed the entrance exam for the West Square Central School, but left at 15 to work, first as a clerk, and from 1932 as a fur salesman at the John Lewis Oxford Street store. He continued his education in evening classes held by the London County Council, the Workers' Educational Association and the National Council of Labour Colleges. In 1938 he began working for the Transport and General Workers' Union as a ledger clerk. A year later he was appointed District Organiser for Watford. Brown volunteered for the RAF at the outbreak of the Second World War, but like other trade union officials was kept in his civilian job by Minister of Labour Ernest Bevin. From 1940 he worked as a temporary civil servant in the Ministry of Agriculture. In 1945 he was elected Member of Parliament for Belper. He served as Parliamentary Private Secretary for George Isaacs, and in 1947 for Hugh Dalton. Brown was appointed Joint Parliamentary Secretary to the Board of Agriculture and Fisheries, despite launching an unsuccessful plot to replace Attlee with Ernest Bevin. In 1951 he was appointed Minister for Works.

After Labour lost the 1951 general election and his subsequent drop from a ministerial salary to a parliamentary salary, Brown considered leaving parliament to return to being a trade union official. However in 1953 he was hired as a consultant for the Mirror Group, and the retainer allowed him to stay in politics. He was a supporter of Hugh Gaitskell and an opponent of Aneurin Bevan. In 1956 he ran for post of Party Treasurer but was narrowly defeated by Bevan. In 1960 he was elected Deputy Leader of the Labour Party. Brown ran for the party leadership after Gaitskell's death in 1963, getting through to the second round of voting, but his reputation for drinking and volatility undermined his campaign and he lost to Harold Wilson. After the 1964 election victory Brown served in Wilson's Cabinet as Secretary of State in the newly created Department for Economic Affairs. During the 1966 financial crisis, Brown supported devaluation. When the Cabinet voted against it, Brown sent a letter of resignation to Wilson, which Wilson returned so that he could claim he had not received it. Brown was eventually persuaded to withdraw his resignation. In August 1966 he was appointed Foreign Secretary, and was behind Britain's 1967 application to join the European Economic Community, succeeded in restoring diplomatic relations with Egypt, and was involved in drafting the United Nations Security Council resolution 242 following the Six-Day War. He resigned as Foreign Secretary in 1968 following an argument with Wilson.

In the 1970 general election he lost his seat to the Conservative Party candidate Geoffrey Stewart-Smith. He received a peerage in the Dissolution Honours List, taking the title Lord George-Brown of Jevington in the county of Sussex. He left the Labour Party in 1976 in protest against a government bill to restore certain forms of legal rights to trade union 'closed shops'. He became President of the Social Democratic Alliance in 1981, but did not join the Social Democratic Party for another four years.

Brown was married once, to Sophia Levene in 1937, with whom he had two daughters, Frieda and Patricia. They separated in 1982. From 1982 until his death Brown lived with his secretary Margaret Haimes. He died in 1985 in the Duchy Hospital in Truro.