Bruun spent his childhood in village of Säiniö on the Carelian isthmus. In the war years his family was forced to move to Helsinki, where he later enrolled in the Central School of Industrial Design. He graduated as a graphics designer in 1950.
After graduation, Bruun worked for three years as an exhibition designer and advertisement artist. In 1953 he founded his own design studio, where he produced the most of his work.
In his work, Bruun mostly features the Finnish nature in all its richness and beauty. Particularly prominent motives include the marine eagle, the Saimaa seal and the bear. The Saimaa seal is the symbol of the Finnish nature preservation association, whose logo Bruun designed.
Bruun also submitted a proposal for the design of the Euro banknotes, featuring various kinds of animals. This proposal was rejected in favour of Robert Kalina's proposal featuring European architecture.
In the early days of the 1986 banknote series, Bruun and his wife were visiting Stockholm, Sweden. They needed to exchange Finnish Markka notes to Swedish krona, and had some of the new Markka notes with them. The cashier, never having seen the new notes before, asked if they were genuine. "Of course they are", replied Bruun's wife, "my husband drew them himself!"