Avraham ("Boolie") Yehoshua was born to a fifth-generation Jerusalem family of Sephardi origin. His father, Yaakov Yehoshua, was a scholar and author specializing in the history of Jerusalem. His mother, Malka Rosilio, immigrated from Morocco in 1932. He grew up in Jerusalem's Kerem Avraham neighborhood.

Yehoshua served as a paratrooper in the Israeli army from 1954 to 1957. He attended Gymnasia Rehavia. After studying literature and philosophy at the Hebrew University of Jerusalem, he began teaching. He lived in Jerusalem's Neve Sha'anan neighborhood.

From the end of his military Service, Yehoshua began to publish fiction. His first book of stories, Mot Hazaken (The Death of the Old Man) was published in 1962. He became a prominent figure in the "new wave" generation of Israeli Writers who differed from earlier Writers in their focus on the individual and interpersonal rather than the group. Yehoshua names Franz Kafka, Shmuel Yosef Agnon, and william Faulkner as formative influences. Harold Bloom wrote an article about Yehoshua's A Late Divorce in the New York Times, and also mentions it in his The Western Canon.

From 1963 to 1967, Yehoshua lived and taught in Paris and served as the General Secretary of the World Union of Jewish Students. Since 1972, he has taught Comparative and Hebrew Literature at the University of Haifa, where he holds the rank of Full Professor. In 1975 he was a writer-in-residence at St Cross College, Oxford. He has also been a visiting professor at Harvard (1977), the University of Chicago (1988, 1997, 2000) and Princeton (1992).

According to La Stampa, before the 2008–2009 Israel-Gaza conflict he published an appeal to Gaza residents urging them to end the violence. He explained why the Israeli operation was necessary and why it needed to end: "Precisely because the Gazans are our neighbors, we need to be proportionate in this operation. We need to try to reach a cease-fire as quickly as possible. We will always be neighbors, so the less blood is shed, the better the Future will be. Yehoshua added that he would be happy for the border crossings to be opened completely and for Palestinians to work in Israel as part of a cease-fire.

Yehoshua is an Israeli Peace Movement Activist. He attended the signing of the Geneva Accord and freely airs his political views in essays and interviews. He is a long-standing critic of Israeli occupation but also of the Palestinians. He and other intellectuals mobilized on behalf of the dovish New Movement before 2009 elections in Israel.