Born in Manchester, United Kingdom, in 1928, Avner first reached British Mandatory Palestine in 1947. He fought in the Siege of Jerusalem during the 1948 Arab-Israeli War, and was amongst the founders of Kibbutz Lavi in 1949. He moved to Jerusalem in 1956 and joined the Israeli Foreign Service in 1958.

During his lengthy career, Avner served in diplomatic positions at the Israeli Consulate in New York City, and the Israeli Embassy in Washington D.C.. In 1983, he was appointed Ambassador to the UK and Non-resident Ambassador to the Republic of Ireland. He returned to Israel in 1988, before serving as Ambassador to Australia between 1992 and 1995.

Avner served as Speechwriter and Secretary to Prime Ministers Levi Eshkol and Golda Meir, and Advisor to Prime Ministers Yitzhak Rabin, Menachem Begin, and Shimon Peres. In September 2010, he authored The Prime Ministers: An Intimate Narrative of Israeli Leadership, in which he shares his first-hand experiences with Israeli leaders at critical moments of decision-making and diplomacy. The Jerusalem Post called the book "the ultimate insider's account.". Avner is also author of The Young Inheritors ... a Portrait of Israel's Children.

In 1995 the Yehuda Avner Chair in Religion and Politics was established at Bar-Ilan University, Ramat Gan, Israel. Avner is a fellow of the Jerusalem Center for Public Affairs and a member of the Ambassadorial Appointments Committee.