Beginning to play the clarinet at the age of 11, but had take up the saxophone by the time he left school and then turned professional. In 1949 he performed at the Paris Jazz Festival, and played with Charlie Parker when he made his tour of Sweden in 1950. Later in 1953, he recorded with visiting American players such as James Moody, Art Farmer and Clifford Brown. Domnérus worked with the Swedish Radio Big Band from 1956 to 1965 as a featured soloist, and wrote for television and films. He also recorded extensively over the course of his career with Bengt Hallberg. Together with fellow Swedes Bengt-Arne Wallin, Rolf Ericson and Åke Persson (the latter two both former members of Duke Ellington's Orchestra), he participated at the Jazz Workshops, organised for the Ruhrfest in Recklinghausen by Hans Gertberg from the Hamburg radio station.
Domnérus' health declined in his last years and he was forced to retire from playing.