Tzvi Avni was born in Saarbrücken, Germany in 1927. In 1935, four months after the Saar was reclaimed by Germany under the Nazis, he immigrated to Mandatory Palestine with his parents.
His interest in music began to develop around that time, but circumstances did not allow for his musical education to take the conventional route. Instead, he taught himself to play the harmonica, mandolin and recorder. On these instruments he began to compose short pieces, and, not knowing how to read a single note, he came up with his own method of writing music.
In addition to music, he began to draw his surroundings, and developed a lifelong interest in art, which became intertwined with his music. Many of his compositions are inspired by works of twentieth-century artists.
In 1943, he began to study piano and music theory. Among his teachers were pianist Frank Peleg and composer Abel Ehrlich. He went on to study at the Music Academy in Tel Aviv under Abel Ehrlich, while serving in the Israel Navy. He also studied with composers Paul Ben-Haim and Mordecai Seter, under whose direction he graduated from the Tel Aviv Music Academy in 1958.
During these years Avni made a living by teaching music at various elementary schools and high schools. He eventually became Director of the Lod Municipal Conservatory, and later Director of the Central Music Library in Tel Aviv. For fifteen years he was the editor of Gitit, the journal of the Israeli branch of Jeunesses Musicales, and later became chairman of the Israel Jeunesses Musicales in 1993, a position he still fills today.
In 1949 he married Pnina Grodnai, a singer and poet. In 1961 he set one of her poems, "Saeni Bemachol", to music, and the song went on to win that year's Israel Song Festival. Pnina died of cancer in 1973.
The mid-1950s saw the first performances of Avni's works in Israel. In 1962 he furthered his studies in the USA, and with a recommendation from Edgar Varèse, began to study electronic music at Columbia University, under the direction of Vladimir Ussachevsky. In the summer of 1963 he received a scholarship to the Tanglewood Music Center, studying composition with Aaron Copland and Lukas Foss.
From 1971 to 2015 he taught theory and composition at the Jerusalem Academy of Music and Dance. He founded and directed the Academy's electronic music studio. In 1976 he was appointed Professor of Theory and Composition.
In 1979 he married Hanna Yaddor, a journalist and translator who later became the culture and music writer for Maariv. The couple had two children, Shiran and Eylon. Tzvi and Hanna collaborated on The Three-Legged Monster, Hanna's story set to music that introduces young listeners to the instruments of the orchestra.
During the years 1993-1995 he spent a sabbatical with his family in the USA, serving as Visiting Professor at Northeastern University and at Queens' College, New York.
Hanna passed away in 2005. In 2017 he married Dvora Finkelstein.
Avni's music has been awarded many prizes. In 1966 his work Meditations on a Drama received the ACUM prize, and was then performed by many orchestras in Israel and abroad. In 1973 he was awarded the Tel Aviv Municipality's Engel Prize for his composition Holiday Metaphors. His Sonata No. 2 for piano, Epitaph, won the ACUM prize in 1981. In 1986 he was awarded the ACUM Lifetime Achievement Award, and later the Israel Prime Minister Prize for Composers in 1998. He also won the Küstermeier Prize by the Israeli-German Friendship Association in 1990 and the Culture Prize of the Saarland in 1999. In 2001 Avni was awarded the Israel Prize, the greatest honor bestowed upon an artist in Israel. He was also awarded the EMET prize in 2015.
Avni's early works were influenced by the "Eastern Mediterranean" style that was dominant in Israel's art music scene in those years, characterized by dance rhythms and tonal-modal elements in harmony and melody. In the beginning of the sixties, his compositions began to be influenced by his interest in electronic music and the more radical approaches he met during his stay in the United States between 1962-64. By the mid-seventies his works took on a new approach towards more tonal elements. Many of his works relate to the visual arts, due to his special relationship with contemporary painting. Some also see in his later works typical Jewish Eastern and European elements.