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 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).
Yehoshua is married to Rivka, a clinical psychologist and psychoanalyst. They have a daughter and two sons, and six grandchildren.