Ivan Albertovich Puni was born in his family summer residence in Kuokkala Settlement (later Grand Duchy of Finland in the Russian Empire, now Repino in Russia). His parents were natives of Italy and his paternal grandfather Cesare Pugni was a well-known ballet composer. His father Albert (Andrey in Orthodoxy) Puni was a violoncellist in the Mariinsky Theater.
In 1915-1916 Ivan Puni was a member of the creative union of avant-garde artists “Supremus” founded by Kazimir Malevich. His apartment in his father’s house at 1, Gatchinskaya Street in St.Petersburg., where with his wife from 1913 to 1915, after returning from Paris, was a popular venue for meetings of artists and poets, avant-gardists and futurists.
In 1917 he was the initiator of the exhibition “0,10”, which marked the transcendence of Russian artists from cubism to suprematism.
Along with other suprematist artists Puni cooperated with arts and crafts cooperative societies in villages Verbovka and Skoptsy.
In 1919 Ivan Puni was a teacher in the Art Institute in Vitebsk under supervision of Marc Chagall.
Ivan Puni was married to Ksenia Boguslavskaya, who was also an avant-garde artist, as well as a designer and a poetess. In the early 1920s the couple emigrated to Germany and then to France. During that period Ivan Puni subscribed his works in the French style Pougny (unlike the initial Italian writing of his surname Pugni).
In 1946 Ivan Puni became the citizen of France. The artist died in Paris on December, 28th, 1956.