Alexander George Montagu Cadogan was born in London on 24 November 1884, the ninth and youngest child of George Henry Cadogan, 5th Earl Cadogan, and Lady Beatrix Jane Craven. Cadogan was educated at Eton College, then at Balliol College, Oxford, and took a second-class degree in History in 1906. In 1912 he married Lady Theodosia Louisa Augusta Acheson (the third daughter of Archibald Brabazon Sparrow Acheson, 4th Earl of Gosford), with whom he had one son and three daughters.

Cadogan came top of the competitive examinations for the diplomatic service in 1908 and in January 1909 was posted as attaché to the embassy in Constantinople, where he was promoted to Third Secretary in 1910. He was transferred to Vienna in April 1913 and returned to London after Britain declared war on Austria-Hungary in August 1914. Thereafter, he spent nearly two decades in the Foreign Office. Between January 1919 and March 1920 he was private secretary to Cecil Harmsworth, Parliamentary Under-Secretary of State for Foreign Affairs, during which time he was promoted to First Secretary. In 1923 Cadogan was made head of the League of Nations section of the Foreign Office and posted to Geneva as Assistant, later Secretary-General, to the British Delegation. He was appointed Acting Counsellor in 1926 and Counsellor in the Foreign Office in 1928, and Adviser on League of Nations Affairs in 1930. In 1933 Cadogan accepted a post in the diplomatic corps as the British Envoy Extraordinary and Minister Plenipotentiary at Peking. He was knighted and formally appointed as Minister to the China legation in January 1934. In June 1935 the legation was upgraded to embassy status, and Cadogan was promoted to Ambassador.

Cadogan returned to London at the invitation of Foreign Secretary Anthony Eden in 1936, becoming Deputy Under-Secretary of State for Foreign Affairs (1936-1937), then Permanent Under-Secretary of State for Foreign Affairs (1938-1946). During the Second World War, Cadogan was present at the major inter-allied conferences alongside Churchill and Eden, and frequently also attended Cabinet meetings.

Cadogan left the Foreign Office in February 1946, having been appointed the first Permanent Representative of the U.K. Government at the United Nations in New York. He retired from the Foreign Service in June 1950, and became the first civil servant to receive the Order of Merit in 1951. Subsequently, Cadogan was nominated as one of three government directors of the Suez Canal Company (1951-1957); served as a Director of the National Provincial Bank (1951-1964); and was made Chairman of the Board of Governors of the B.B.C. (1952-1957). In January 1956 he was appointed Chairman of the Commonwealth-American Current Affairs Unit, a branch of the English-Speaking Union. Cadogan largely retired from public life after the end of his terms with the Suez Canal Company and the B.B.C., devoting himself to painting, gardening, and golf.

He was awarded CMG (1926), CB (1932), KCMG (1934), GCMG (1939), and made a Privy Councillor in 1946 and an Honorary Fellow of Balliol College, Oxford, in 1950. He died in 1968.