He founded the journal Probability and Mathematical Statistics and served as rector of the University of Wrocław.

During World War II the town came under Soviet control, and was annexed by Ukraine; after the war, Urbanik's family moved to Brzeg, which remained Polish.

Beginning in 1948, Urbanik studied mathematics and physics at the University of Wrocław, where he was mentored by Hugo Steinhaus and Edward Marczewski.

His work in probability theory included work on random variables in compact groups, connections between measurability and connectivity, generalized convolutions, and decomposability semigroups.

He also studied stochastic processes, information theory, universal algebra, and functional analysis.