Bakshi-Doron was born in Jerusalem in pre-State Israel and studied in several prominent Religious Zionist yeshivot. From 1970 to 1972, after receiving his rabbinical ordination, Bakshi-Doron served as a community rabbi in Bat Yam before being elected Chief Rabbi of Bat Yam in 1972. In 1975, he was appointed Chief Rabbi of Haifa, a position he held until 1993.
In 1993, Bakshi-Doron was elected the Sephardic Chief Rabbi of Israel. He held the position until 2003.
Rabbi Bakshi-Doron has written dozens of articles dealing with religious issues. His first book (1982) researches halachic questions, and the second (1989) and third (1995) volumes deal with daily halachic issues and include orations given by him on special occasions. He serves as president of the Sephardic Community Committee, as president of various charity foundations and is a member of the directorate of LIBI.
Bakshi-Doron is a widower; his wife Esther, the daughter of the former Chief Rabbi of Akko, died in 2005. The two had ten children.