Cengiz grew up in a military family, often traveling across the country. He began playing violin in high school, enrolling at Ankara State Conservatory in 1952 to join Ahmed Adnan Saygun's class. The following year, after his father became a military attaché in London, Cengiz relocated to the United Kingdom with his family, attending The Guildhall School Of Music & Drama between 1953 and '56. Subsequently, he returned to Turkey and finished his degree at Ankara State Conservatory in 1960. In later years, Tanç trained as a "tonmeister" under renowned Turkish-American composer and electronic music pioneer Bülent Arel (1919—1990).

Between 1968 and 1973, Cengiz Tanç worked as the Western Music Branch Manager at The Guildhall School Of Music & Drama's Ankara Radio. He then served as the State Opera and Ballet's lead dramaturgist. In 1976, Tanç moved to Istanbul, appointed Head of the Composition Department at the Mimar Sinan Fine Arts University (MSGSÜ). Cengiz Tanç lived in the USA on a Fulbright research scholarship in 1984–85, studying with Vincent Persichetti and Milton Babbitt.

Cengiz Tanç worked across multiple genres, writing for chorus, orchestra, and chamber ensembles and authoring several operas and ballets. Initially inspired by Turkish folk music and contemporary composers, he gradually evolved beyond traditional compositional concepts and the influence of Igor Stravinsky, Béla Bartók and others. Tanç established an original understanding of sequencing and used various complex forms in his later works, such as modal tetrachords.