He began to study scenography at the Prague Conservatory and architecture at the Academy of Applied Arts.
Svoboda became the principal designer at the Czech National Theatre in 1948 and held that position for more than 30 years.
His multimedia installations Laterna Magika and Polyekran, realized together with director Alfréd Radok and his brother Emil on the occasion of the Expo 58 in Brussels, allowed him to be internationally known.
Svoboda is also responsible for introducing modern technologies and materials such as plastics, hydraulics and lasers into his designs.
Svoboda's honors and awards include honorary doctorates from the Royal College of Arts in London, Denison and Western Michigan universities in the United States, and awards from the United States Institute for Theatre Technology (USITT).