He was born in Kallaste, in the Governorate of Livonia of the Russian Empire (nowadays in Tartumaa, Estonia).
In 1944, as the Red Army was approaching, Rannit emigrated to Germany, where he continued with his studies at the Institute of Applied Arts in Freiburg (1946–1950).
[1] In 1956, he defended his master's thesis on arts history (annotated critical biography of Ciurlionis) at Columbia University in New York.
He worked as a research fellow and curator of Slavic and Eastern European collections at the University of Yale.
He was a founding member of International Association of Arts Critics, represented the Estonian authors at the PEN club, and was part of the editorial staff of Continent.