Engel was born, (and named Yuliy Dmitrievich Engel) in Berdyansk, now in Ukraine. Unlike most Jewish families of the period, he grew up outside of the Pale of Settlement, the area designated by the Czar as legal for Jewish residence. His parents were secular Jews. Engel studied law at the Kharkiv National University, and later, at the urging of Pyotr Ilyich Tchaikovsky, who heard his compositions, entered the Moscow Conservatory.