Born to Hacham Meir Davidi, he continued the tradition of a learned scholar and after moving to Tehran, became a more prominent community leader in his own right. In the late 1970s, Davidi, along with the late chief rabbi, Hacham Yedidia Shofet, made annual visits to the Shah Mohammad Reza Pahlavi, as representatives of the Jewish community. In 1979, shortly after the Islamic revolution, Davidi and Shofet, along with a few other members of the Jewish community of Tehran, met with the new leadership of the Islamic Republic in order to preserve the rights of the Jewish community. Among Persian Jews, he has been known as "Hacham Uriel".
Hacham Uriel Davidi served as the chief rabbi of Iran after Hacham Shofet left, from 1980 to 1994. He gave weekly religious lectures on Saturday afternoons in Tehran's Darvaz-e Dolat Synagogue during this time. He also performed wedding ceremonies and functioned as a 'mohel'. On January 17, 1994, he moved to Jerusalem, Israel.