Radoslav Zuk first studied music in Austria before moving to Canada to pursue a bachelor's degree in Architecture from McGill University. He graduated from McGill in 1956. From 1956 until 1959 he worked with the Montreal firm of Rother Bland Trudeau - alongside the Director of the McGill School of Architecture John Bland - and worked on such projects as Ottawa City Hall. He also worked briefly in London, contributing to the design of the United States Embassy in London. Subsequent to these pursuits Zuk left Canada to pursue a Master's degree in architecture at the Massachusetts Institute of Technology, which he completed in 1960. Following graduation from the American school, Zuk was quickly hired by the University of Manitoba Faculty of Architecture, where he taught as Assistant Professor from 1960 to 1964. Zuk registered with the Manitoba Association of Architects in January of 1961 and in his brief time here created a number of works for the Ukrainian Catholic Archeparchy of Winnipeg which display his unique and notable fusion of modernist design and elements of traditional Ukrainian architecture.

Following his departure from Winnipeg, Zuk returned to McGill University to teach, where he was the recipient of the Faculty of Engineering Ida and Samuel Fromson Award for Outstanding Teaching. During this period the architect also further established himself as a leader in religious design. In 1986 Zu won a Governor General's Medal for Architecture for St. Stephen's Byzantine Ukrainian Catholic Church in Calgary and earning, in 2011, the State Prize of Ukraine for Architecture for the Church of the Nativity of the Most Holy Theotokos, Lviv, Ukraine. He has taught at the University of Toronto and at the McGill University School of Architecture, where he holds the title of Professor Emeritus. He is an Honorary Professor of the Kyiv Technical University of Building and Architecture and a Professor of the Ukrainian Free University in Munich.