He was born in 1912 in Bačka Palanka. He studied law in Belgrade and Paris, where he finished his PhD studies. He was a professor at the Faculty of Economy and Faculty of Law of the University of Belgrade. He was a member of the Communist Party of Yugoslavia since 1935 and participated in the Spanish Civil War. Uvalić was the initiator and founder of the Association of Economists of Serbia and one of its first chairmen. He was the founder and for years, the editor in chief of the first journal of economic theory, Ekonomist. Simultaneously he worked on establishing the Faculty of Economy in Belgrade. Due to his engagement, the first Institute of Economy was also founded in Serbia, where first serious research was realised concerning the economy of Serbia and Yugoslavia.
He was one of the main initiators of the establishment of the Union of Economists of Yugoslavia, and the chairmen of its founding congress. From 1953 to 1960, he was the Yugoslav Ambassador to Norway, Austria and France, and from 1967 the Ambassador to India.
He was the Director of the Institute of Social Sciences from 1960 to 1962. He was elected a corresponding member of the Serbian Academy of Sciences and Arts in 1961. As of 1967, he was the Assistant to the State Secretary for Foreign Affairs, while in 1971, he was once again appointed the Ambassador to India. He was killed in a traffic accident in Iran, on 28 September 1971. He was a recipient of the Commemorative Medal of the Partisans of 1941 (Partizanska spomenica 1941).