Bebluani was born in the mountainous Svanetian village of Chaguri in the Georgian SSR.
He graduated from Tbilisi State Theater Institute in 1979, being tutored by Tengiz Abuladze and Irakli Kvirikadze.
He performed in the Soviet-era movies Our Youth (ღიმილის ბიჭები, 1969), Earth, This Is Your Son (მშობლიურო ჩემო მიწავ, 1980), and Cucaracha (კუკარაჩა, 1982); and directed The Flight of Sparrows (ბეღურების გადაფრენა, 1980), and The Brother (ძმა, 1981).
[1] In 1996, he was one of the producers of A Chef in Love directed by Nana Jorjadze, which became the first Georgian film to be nominated for the Academy Award.
His elder son, Géla Babluani, is also a filmmaker; the younger, Giorgi, is an actor.