Hacham Moshe Soulam was born in Gharadaïa, Algeria, in the Northern Sahara. He was the rabbi of the M'zab region in the south of Algeria and served as the community's spiritual leader, sage, dayan, halakhic adjudicator, shochet and bodeq for over fifty years. He taught in the study house located in his home in Gharadaïa. His students included the poor and destitute, whom he supported materially as well as spiritually. He would wake his students during the night to study Torah during the Hour of Compassion, so that Torah would not be forgotten. He sought to teach them the laws of ritual slaughter (shechita) so that they could, under any circumstances, meet their household as well as financial needs in foreign cities where there might not be any Jews, and preserve their Judaism. His teachings spread, and his students grew up to become rabbis, shochatim, cantors and mohalim in Algeria and beyond. He wrote Torah scrolls himself, working the hides into parchment by hand and preparing the ink with strict precision. He was a talented cantor, and composed poems and piyuttim; he lived an ascetic life and was known for his humility.
Hacham Moshe Soulam passed away on the Festival of Shavuot, during the reading of the Ten Commandments, just as "...Moses rose up to the LORD", his soul ascended on 6 Sivan 5717 (1956). His hilloula is commemorated in the Ahava VeAchva synagogue in Givat Shmuel.
Hacham Moshe Soulam wrote two books, Sefer Yedei Moshe – laws governing ritual slaughter, and VaYishma' Moshe, a collection of sermons.