Rabbi David ben Shlomo ibn Abi Zimra, known as the Radbaz from the initials of his name, was born in Spain in 5239 (1479) into a family of scholars. He was about thirteen when the Jews were expelled from Spain in 1492 and went into exile with his family. In his youth he studied under Rabbi Yosef Saragossi. He lived in Safed and Jerusalem, and also spent time in Fez, Morocco, where he sat on the rabbinical court headed by the Nagid Rabbi Yitzchak HaKohen Sholal.

He then settled in Egypt. In Cairo he became the leader of the community and chief rabbi of Egypt, a post he held for some forty years, serving as head of the court, rosh yeshiva, and overseer of charity and communal property. A successful and independent merchant, he gave generously of his wealth to the poor. He restored the custom of having the chazzan repeat the Amidah aloud after the congregation's silent prayer, and replaced the Seleucid dating still used in Egypt with the reckoning of years from Creation.

His yeshiva in Cairo attracted outstanding students, among them Rabbi Betzalel Ashkenazi, author of the Shitah Mekubetzet, and the Arizal; Rabbi Yaakov Castro (the Maharikash) was also his disciple. A leading halachic authority, he received questions from distant communities. According to the sources he wrote more than three thousand responsa, or even more than ten thousand, most of them lost; those that survive form the Responsa of the Radbaz. He also wrote Yekar Tiferet on Maimonides' Mishneh Torah, Kelalei HaGemara, and kabbalistic works such as Metzudat David, Magen David and Ohr Kadmon.

In old age he left his post in Egypt and moved to Jerusalem, but the heavy taxes imposed on him by the governor forced him to settle in Safed, where Rabbi Yosef Karo held him in great esteem. He lived there for about twenty years and passed away in 5333 (1573), at the age of ninety-four. He was buried in the Old Cemetery of Safed, in the section of the Arizal; his long-forgotten grave was identified in 2015, to the right of the grave of the Mabit.