He studied piano with Marika Laspopoulou and composition with Alekos Kontis at the Hellenic Conservatory in Athens (1922–34), as well as the piano and orchestration with Emilios Riadis in Thessaloniki (1928–29). In 1949 he visited major European music centres on a UNESCO grant and became familiar with new developments in music composition. In particular, in Paris he attended Arthur Honegger's class. Between 1951 and 1961 he taught music at an Athens high school and from 1953 he was professor of counterpoint and composition at the Hellenic Conservatory. He was the first president of both the Greek section of the International Society for Contemporary Music (1964–75) and the Hellenic Association for Contemporary Music (1965–75). Papaioannou played a pivotal role in the inception of the festivals of Contemporary music which were financially backed by various institutions, including the Greek Tourist Organisation and several foreign entities. Papaioannou was the first musician to systematically teach atonal, 12-note and serial techniques before 1970. His compositional career falls into five main phases: Early Impressionist (1932–8), National School (1939–43), Hindemithian neo-classicism combined with elements of Byzantine music (1944–52), 12-note period (1953–1966) and the last period (1966–89) in which he developed an entirely personal technique.