He studied composition in Florian Dąbrowski’s class at the Academy of Music in Poznań, which he completed in 1985.
He has won many composition competitions. In 1985, he received a distinction at the Polish Composers’ Union Competition for an organ work in Kamień Pomorski, in 1986 – a distinction at the Polish Composers’ Union Young Competition, in 1987 – a distinction in the Polish Composers’ Union Competition for a work for organs and two other instruments, and 2nd prize (1st prize was not awarded) in the "Do-Re-Mi ’87" Competition of Contemporary Creativity for Children and Youth, in 1988 – 1st prize (in the symphonic category) and a distinction (in the chamber music category) at the Grzegorz Fitelberg Polish National Composers’ Competition in Katowice. In 1990, he received a distinction at the Ryszard Bukowski Competition in Wrocław, and in 1996 – 3rd prize (1st and 2nd prizes were not awarded) at the Polish Radio Competition for a radio piece. He was also awarded the Young Art Medal (1988) and a special prize for the Waldemar Śmigasiewicz film The Little Prince at the Festival of Feature and Television Films for Children and Youth (1992).
From 1990 to 1996, Zbigniew Kozub served as Deputy Dean of the Department of Composition, Conducting and Theory of Music at the Academy of Music in Poznań, from 1996 to 2002 he was the Dean of that department, since 2005 he has been the Director of the Department of Composition and Theory of Music at the Academy of Music in Poznań. In addition, from 1993 to 99, he was the president of the Poznań Branch of the Polish Composers’ Union and director of the Poznań Music Spring Festival. Between 1999 and 2003 he was a member of the Programme Council of Radio Mercury, and between 2002a nd 2004 he was a member of the Committee of the Artistic Award of the City of Poznań. He also cooperates with the Academy of Fine Arts in Poznań, where he lectures on film music for the students of film animation.
In 1995, he received the PhD degree, in 2002 in habilitation in the field of music (discipline: composition and theory of music) at the Academy of Music in Poznań. On 2nd April 2015, he was nominated a Professor of music.