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 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). 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.
His comment that "Arabs never miss an opportunity to miss an opportunity" (ie, for peace) made after the Geneva peace talks in December 1973, is often quoted.
Abba Eban's brother-in-law is the late Chaim Herzog, the sixth president of Israel. Herzog's son Isaac Herzog is a minister in Israel's Knesset. Eban's cousin, Oliver Sacks, is a neurologist and author and his son, Eli Eban, is a renowned clarinetist who teaches at Indiana University. Eli has two children, Yael and Omri Eban. His nephew, Jonathan Lynn is a filmmaker and script writer known for satirical BBC shows Yes Minister and Yes, Prime Minister. Lynn recounts that the plot of an episode of Yes, Prime Minister, which involved the British Prime Minister bypassing his own Arab-centric bureaucracy by taking the Israeli ambassador's advice, was based on an actual incident narrated to him by Eban.