Hacham Yom Tov Algazi, son of Hacham Israel Yaakov Algazi, was born in 1727 in Izmir, Turkey. He immigrated to Jerusalem with his family in 1735, where his father was to subsequently officiate as Rishon LeZion (1756). Hacham Yom Tov Algazi learned Torah from his father, and studied at the Beit Yaakov Ferara yeshiva with Hacham Yona Navon, author of Nechpa BeChesef, as well as in the Beit El kabbalist yeshiva with Hacham Shalom Shar'abi, known as the RaSHaSH.
In 1758 he was already considered one of the sages of the Neve Shalom yeshiva in Jerusalem and belonged to the Ahavat Shalom Rabbinic Society, headed by Hacham Shalom Shar'abi. Hacham Yom Tov Algazi was appointed to the Great Rabbinic Court of Jerusalem and was one of the leaders of the city's Sephardi community.
He travelled as a rabbinic emissary to Europe and North Africa with Hacham Yaakov Hazzan between 1770 and 1775. During their journey they advised the various communities on matters of Halakha and governance, ordained rabbis and provided approbations for Torah literature, strengthening the communities and their affinity to the Jewish communities in Israel.
During their mission they discovered a manuscript by Nachmanides on Halakha concerning first-fruits, vows, bread and more, on which Hacham Yom Tov Algazi authored his work entitled Hilkhot Yom Tov. They found additional manuscripts of prominent sages, including one of the book Yad Ramah, written on Tractate Bava Kama, which they were the first to publish, in Salonica, 1790.
In 1776 he took on the post of Rishon LeZion, and in 1977, following the death of Hacham Shalom Shar'abi, was appointed head of the Beit El kabbalist yeshiva, a position he retained to the end of his days.
In 1798 Napoleon began his campaign in the Land of Israel. The Jews of Jerusalem, suspected of sympathizing with the French, were in danger, in particular after Napoleon declared his intention of returning the Land of Israel to the Jews. Hacham Yom Tov Algazi assembled the Jews at the Western Wall to prayer for the war's end, who volunteered to fortify and buttress the city walls.
As a result of the war, famine and epidemics raged; Hacham Yom Tov Algazi, despite his advanced age, was forced to travel abroad again to raise money for the community. His mission lasted a year.
Hacham Yom Tov Algazi passed away on 2 Adar Aleph, 5562 (1802) and was buried in the Mount of Olives cemetery in Jerusalem, next to the tombs of his father, Rishon LeZion Hacham Israel Yaakov Algazi, and of his teacher, Hacham Shalom Shar'abi.
Hacham Yom Tov Algazi authored several books, including Simchat Yom Tov - responsa, in two volumes; Kedushat Yom Tov – responsa and original commentary, Yom Tov DeRabbanan – sermons, and Peirush MeHareit - on the Torah.