Born in Borgentreich in Westphalia in 1825, the son of Samuel Moses and Hanna Rosenbaum, Moses Rosenbaum immigrated to the United States at the age of thirteen, settling in San Francisco in 1850. With his brother Albert and Joseph Brandenstein, he established a tobacco firm, A. S. Rosenbaum & Co., at one time the largest in the West. Their business partner would marry the Rosenbaums’ sister Jane, and in 1854 Moses married Bertha Kohlberg with whom he had six children.

Rosenbaum served as the secretary of the California Republican State Central Committee and volunteered as a firefighter with the Howard No. 3 Fire Company. He was a philanthropist and active in Jewish organizations in the city and a member of Temple Emanu-El.