Ivasyuk was born in Kitsman, Chernivtsi Oblast. His father Mykhaylo Ivasyuk was a well-known writer from Bukovyna. His mother Sofiya Ivasyuk, from the Zaporizhia Oblast by birth, was a teacher in a local school. He had two sisters, Halyna (b. 1944) and Oksana (b. 1960). As early as the age of five, Volodymyr began learning to play the violin at a music school. Later, he learnt to play the piano as well. In 1964 he created an ensemble - "Bukovyna" - in his school and wrote their first songs, the first of which was "Lullaby".