At the age of seven, Bazylevych attended an art club at the Palace of Culture of the Metallurgical Plant in Zhdaniv (now Mariupol). During the German occupation (1943–1945), he was forced into labor in Germany together with his parents; his father was killed in May 1944 during a bombing raid.

From 1947 to 1953, Bazylevych studied at the Kharkiv Art Institute, specializing in book and easel graphics. Among his teachers were Yosyp Daits, Hryhorii Bondarenko, Adolf Strakhov, Vasyl Myronenko, and others. His diploma project — illustrations for The Bukovynian Story by Ihor Muratov — demonstrated his ability to merge folk traditions with professional graphic mastery.

After moving to Kyiv in 1953, Bazylevych began collaborating with leading publishing houses (Molod, Veselka, Dnipro, Mystetstvo, Radianska shkola, among others), as well as with the printmaking workshop of the Monumental and Decorative Arts Combine. Since joining the Union of Artists of Ukraine in 1956, he participated in all-Union and international exhibitions. His solo exhibitions were organized in Kyiv in 1961 and 1996.

For over a decade (1958–1968), Bazylevych, together with other artists, created illustrations for Kotliarevskyi’s Aeneid — more than 130 drawings first published in 1968 by Dnipro Publishing to mark the poet’s 200th anniversary. Printed in an edition of 5,000 copies, the book sold out within days and was reprinted 17 times. Bazylevych’s illustrations for the Aeneid gained immense popularity and remain among the most recognizable visual interpretations of the Cossack Aeneas in Ukrainian art.

Bazylevych’s graphics combine folklore motifs, burlesque, and subtle humor with profound historicism. He skillfully “encoded” erotic episodes of Aeneid through hints and symbolism, circumventing censorship. Art historians describe his visual style as a “hybrid of images” that blends antiquity, 19th-century ethnography, and the charm of the 1960s generation.

His works are held in the National Art Museum of Ukraine in Kyiv, the Museum of Books and Printing of Ukraine, the Alupka Art Gallery, as well as private collections in Ukraine and abroad. His Aeneid illustrations have been repeatedly shown in retrospectives.

Anatolii Bazylevych shaped one of the most recognizable visual identities of Ukrainian book graphics of the 20th century. His illustrations continue to inspire, influencing new generations of artists and readers.