He is the son of engineer Toivo Ilmari Leiviskä and teacher Sonja Jämsén-Astala. Leiviskä studied architecture at the Helsinki University of Technology, qualifying as an architect in 1963. After taking on teaching commitments, he established his own office in 1964, while simultaneously working as a teaching assistant. 

His collaboration with architect Bertel Saarnio of Kouvola Town Hall in 1964 won and architectural competition and brought a large amount of attention  to the designer, the building was regarded as one of the most significant public buildings in Finland during the 1960s. His work continued on throughout the 1970s, 1980s and 1990s, developing churches across Finland. 

His buildings are monumental, yet still possess the quality of intimacy, with light taking a central role in the architecture. Further to his talent for using natural light in his architecture, Leiviskä is also a skilled lighting designer. He experiences interiors as “instruments played by light.” His mature style combines the sensitivity to the dramatics of natural light of German Baroque churches, with compositional principles of Dutch De Stijl architecture of the 1920s. 

He has been quoted saying:

"Architecture is closer to music than to the visual arts. To qualify as architecture, buildings, together with their internal spaces and their details, must be an organic part of the environment, of its grand drama, of its movement and of its spatial sequences. To me, a building as it stands, "as a piece of architecture" is nothing. Its meaning comes only in counterpoint with its surroundings, with life and with light."