From 1959 to 1964, Terzakis studied composition with Yannis Papaioannou at the Athens Hellenic Conservatory, followed by five years spent at the Hochschule für Musik in Cologne, Germany where he studied composition with Bernd Alois Zimmermann and electronic music with Herbert Eimert.
Works by Terzakis have been performed at the International Society for Contemporary Music Festival in Basel (1970), the Darmstadt Artists' Colony summer courses (1970) and the Hamburg Das Neue Werk series (1972).
In 1980, he began to organize summer courses in Western and south-eastern European music in Nafplion.
From 1994 to his retirement, he held the chair for composition at the Leipzig Felix Mendelssohn College of Music and Theatre.
In recent years, Terzakis's view of Western harmony, polyphony and the tempered system as constituting only an extended episode in the evolution of music has increasingly led him to an essentially monophonic output.