Kubilius was born in Fermos village, Eržvilkas county, Jurbarkas district municipality, Lithuania on July 27, 1921. He graduated from Raseiniai high school in 1940 and entered Vilnius University, from which he graduated summa cum laude in 1946 after taking off a year to teach mathematics in middle school.

Kubilius has had simultaneous careers at Vilnius University and at the Lithuanian Academy of Sciences. He continued working at the university after receiving his Masters's degree in 1946, and worked as a lecturer and assistant professor after receiving his Candidate degree in 1951. His thesis was written under Yuri Linnik. He received the Doctor of Science degree (habilitation) in 1957 from the Steklov Institute of Mathematics in Moscow.

In 1958 he was promoted to professor and was elected rector of the university. He retired from the rector's position in 1991 after serving almost 33 years, and remained a professor at the university.

Kubilius's scientific work has been in the areas of number theory and probability theory. The inequality and the model in probabilistic number theory are named after him. A monograph devoted to probabilistic number theory was translated into English in 1964 and became very influential.

Kubilius organized the first mathematical olympiad in Lithuania in 1951 and he wrote books of problems for students to use in preparing for the olympiads and the textbooks for students. He was the president of the Lithuanian Mathematical Society.

Professor Jonas Kubilius passed away on 30 Oktober 2011, one month after the fifth Conference in Analytic and Probabilistic Number theory in Palanga organized in his honour.