Born in Cape Town, South Africa, Eban moved to England at an early age. He was educated at St Olave's Grammar School, Southwark before studying Classics and Oriental languages at Queens' College, Cambridge where he achieved a triple first. As a child, he recalls being sent to his grandfather's house every weekend to study the Hebrew language and Biblical literature. During his time at University and afterwards, Eban was highly involved in the Federation of Zionist Youth and was editor of its ideological journal "The Young Zionist". After graduating with high honours, he researched Arabic and Hebrew as a Fellow of Pembroke College from 1938–1939. At the outbreak of World War II, Eban went to work for Chaim Weizmann at the World Zionist Organization in London from December 1939. A few months later he joined the British Army as an intelligence officer, where he rose to the rank of major. He served as a liaison officer for the Allies to the Jewish Yishuv of Palestine. Drawing on his linguistic skills, in 1947 he translated from the original Arabic, Maze of Justice: Diary of a Country Prosecutor, a 1937 novel by Tawfiq al-Hakim.
Eban moved back to London briefly to work in the Jewish Agency's Information Department, from where he was posted to New York, where the General Assembly of the United Nations was considering the "Palestine Question". In 1947, he was appointed as a liaison officer to the United Nations Special Committee on Palestine, where he was successful in attaining approval for the partition of Palestine into Jewish and Arab segments—Resolution 181. At this stage, he changed his name to the Hebrew word Abba (however it was seldom used informally), meaning "Father", as he could foresee himself as the father of the nation of Israel. Eban spent a decade at the United Nations, and also served as his country's ambassador to the United States at the same time. He was renowned for his oratorical skills. In the words of Henry Kissinger:
"I have never encountered anyone who matched his command of the English language. Sentences poured forth in mellifluous constructions complicated enough to test the listener’s intelligence and simultaneously leave him transfixed by the speaker’s virtuosity."
His polished presentation, grasp of history, and powerful speeches gave him authority in a United Nations that was generally skeptical of Israel or even hostile to it. He was fluent in ten languages. In 1952, Eban was elected Vice President of the UN General Assembly.
Eban left the United States in 1959 and returned to Israel, where he was elected to the Knesset (the Israeli parliament) as a member of Mapai. He served under David Ben-Gurion as Minister of Education and Culture from 1960 to 1963, then as deputy to Prime Minister Levi Eshkol until 1966. Through this entire period (1959–1966), he also served as president of the Weizmann Institute in Rehovot.
From 1966 to 1974, Eban served as Israel's foreign minister, defending the country's reputation after the Six-Day War. Nonetheless, he was a strong supporter of giving away parts of the territories occupied in the war in exchange for peace. He played an important part in the shaping of UN Security Council Resolution 242 in 1967 (as well as UN Security Council Resolution 338 in 1973). Among others high level contacts, Pope Paul VI received Foreign Minister Abba Eban in 1969.
Eban was at times criticized for not voicing his opinions in Israel's internal debate. However, he was generally known to be on the "dovish" side of Israeli politics and was increasingly outspoken after leaving the cabinet. In 1977 and 1981 it was widely understood that Shimon Peres intended to name Eban Foreign Minister, had the Labor Party won those elections. Eban was offered the chance to serve as Minister without Portfolio in the 1984 national unity government, but chose to serve instead as Chair of the Knesset's Foreign Affairs and Defense Committee from 1984 to 1988.