Prime Minister Binyamin Netanyahu called Yosef one of the "great halachic [Jewish law] authorities of our generation," The Jerusalem Post reported. "The Jewish people lost one of the sages of this generation."
President Shimon Peres visited Yosef at Hadassah Hospital, where the rabbi was recently admitted after his health deteriorated, hours before he died.
The religious Shas party was founded in 1984.
Yosef, combining religious and political leadership, became one of the most powerful religious figures in Israel's history, The Times of Israel said.
Yosef is survived by 11 children and numerous grandchilren, Ynetnews.com reported.