Bryggman studied at the Design School of the Turku Art Society and at the Helsinki Polytechnic School (graduated 1916). Shortly thereafter he collaborated on the design of a number of important works, including the Helsinki War Memorial.

With the Finnish architect and designer Alvar Aalto he organized the 1929 exhibition celebrating the 700th anniversary of the city of Turku, an event that many consider to be the beginning of modern architecture in Finland. His important works during the 1930s include the Vierumäki Sports Club (1930–36) and the library of the Turku Academy (1935), both notable for their smooth, undecorated surfaces. His most important work is considered to be the chapel of the Turku cemetery (1938–41), which, though in the functionalist idiom, makes a strong emotional appeal, particularly through the use of light entering the interior as an architectural element.

Bryggman's later works, showing considerable romanticism in their use of indigenous materials and traditional forms, include houses at Pansio, near Turku (1946), the Students' Union and chemistry laboratory of Turku Academy (1948–50), and the Water Tower at Riihimäki (1951–52).