Michał Ulam was born into a Jewish family in Lviv. He graduated from the Industrial School and, in 1903, received a license for independent construction work. Ulam studied at the Munich Academy of Fine Arts and later served as vice-president of the Chamber of Commerce and Industry in Lviv from 1929 to 1935. He also initiated the establishment of the Central Union of Merchants and Industrialists and chaired several Jewish professional organizations.
In 1903, Ulam established his own architectural and construction firm. The firm quickly grew, carrying out projects both by Ulam and by other architects. His collaborators included Tadeusz Obmiński, Roman Feliński, and Ferdinand Kassler. Ulam was honored with the Golden Cross of Merit for his contributions to the Eastern Trade Fairs in Lviv. His nephew, Stanislaw Ulam, became a renowned mathematician and physicist and one of the developers of the hydrogen bomb in the United States.