Rabbi Yosef ben Meir HaLevi ibn Migash, known by the acronym Ri Migash, was born in 4837 (1077), probably in Seville, in al-Andalus; other sources place his birth in Granada. His family, a distinguished one, came from Granada. As a child he studied Torah with his father, Rabbi Meir HaLevi ibn Migash, and with Rabbi Yitzchak ibn Albalia.

At the age of twelve he went to Lucena to study under the Rif, Rabbi Yitzchak Alfasi, who had just become head of the yeshiva there. He remained his disciple for fourteen years and received semichah from him. Shortly before his death in 4863 (1103), the Rif appointed him as his successor, passing over his own son, when Rabbi Yosef was only 26 years old. He headed the yeshiva of Lucena for thirty-eight years, until the end of his life.

His fame spread throughout the Jewish world, and students came from Spain and North Africa to learn from him, among them Rabbi Maimon the Dayan, father of the Rambam. The Rambam regarded him as his teacher: unusually for him, he cites him by name in the Mishneh Torah, and in the introduction to his Commentary on the Mishnah he expresses deep admiration for his mastery of the Talmud and the depth of his reasoning. According to Sefer HaKabbalah, he was a man of great humility. Rabbi Yehudah HaLevi composed poems in his praise.

He is the first Sephardic sage whose novellae on the Talmud have come down to us. Only a small part of his work survives: more than two hundred responsa, most of them written in Judeo-Arabic, and his chiddushim on the tractates Bava Batra and Shevuot. His explanations are quoted by the Ramban, the Rashba, the Ritva and in the Shittah Mekubetzet.

He passed away in 4901 (1141) in Lucena.