The artist was born in 1896 in Yelisavetgrad  (now Kropyvnytskyi, Ukraine) or in Kherson. Ivan spent his youth in Kherson and Kharkiv. After the revolution the young man went to Germany and got there artistic education.

In 1924 he held a personal exhibition in Berlin gallery named Kasper (together with Mykola Gloutchenko), in 1925 he joined the exhibition of  New Objectivity  movement in Mannheim, Erfurt and Hamburg. In 1925 the artist moved to Paris. His works were exhibited in the salons of National Fine Arts Society (1925), d’Automne (its member in 1925–1935) des Artistes Indépendants (1926–1935).

In 1927 he sent his works to Jubilee Exhibition of USSR Peoples in Moscow, 1st All-Ukraine exhibition of Revolutionary Art in Kharkiv and All-Ukraine Jubilee exhibition that travelled in many Ukrainian cities. He took part in Russian section of “Contemporary French Art” exhibition in Moscow (1928), Russian art exhibitions in Brussels (1928) and the ones of Paris group of Ukrainian artists in Paris (1932) and Lviv (1933). In 1929 Babij held a personal exhibition in W. Hirshman gallery (paintings, watercolours and drawings).

In 1935–1936 he took part in exhibitions “ Contemporary Portrait” in Galerie de Paris and in Jeu de Paume art centre, exhibiting his canvas “Encyclopaedists of XX Century”, showing the authors of the Great Encyclopedia. In 1930-ies he worked in Africa for a long time, creating portraits, landscapes and ethnographic sketches. His art was reproduced in French magazines. In 1940 his African works were exhibited in Zak gallery.

Ivan Babij died no earlier than 1949 (other version – in 1974).