He was born in Sarajevo and went to primary school in Zenica. Then he went to comprehensive secondary schools in Visoko, Sarajevo and Zagreb. He received a BA degree in the Croatian language and Yugoslav literature from the Faculty of Philosophy of the University of Zagreb. In 1957, he received his Ph.D. with the study Speech in the Valley of River Fojnica.
Brozović worked as an assistant at the Zagreb Theater Academy and as a lecturer at the University of Ljubljana. He was a professor at the Faculty of Philosophy in Zadar from 1956 to 1990. He is one of the authors of the Declaration on the Status and Name of the Croatian Standard Language, which started demolishing Yugoslavian linguistic unitarism and its promotion of a hybrid Serbo-Croatian language.
He is a member of the Croatian Academy of Sciences and Arts. In the late eighties, he was a co-founder and vice-president of the Croatian Democratic Union, which would win the 1990 elections. He was the vice-president of the presidency of the Republic of Croatia and a member of the Croatian Parliament. From 1991 to 2000 he headed the Miroslav Krleža Institute of Lexicography. He edited the Atlas of European and Slavic Dialectology.
His outstanding works are his studies about standard Slavic languages (especially his book Standard Language of 1970). Along with his numerous valuable studies about Croatian dialectology, phonology and comparative history of linguistics, Brozović used the conceptual tools of structural linguistics (Havranek, Trubetzkoy, Jakobson) to present a new picture of Croatian linguistic history, which replaced the rudimentary and often erroneous textbooks which had been using obsolete Neogrammarian terminology and approach.
His work Croatian Language, Its Place among the South Slav and Other Slav Languages, Its Historical Changes as the Language of Croatian Literature (1978) divides the history of the Croatian language into three pre-standard and three standard periods. In the time when it was widely believed that Croatian was standardized around the time of the Illyrian movement and Ljudevit Gaj, Brozović showed that the standardization began around 1600 and greatly developed around 1750.
This work was originally an intro on Savjetovanje o Osnovama nastavnog plana i programa hrvatskog književnog jezika s književnošću za srednje škole, held in hotels "Solaris" in Šibenik, Croatia, 22-24 November 1971, in organization of Republička konferencija Saveza omladine Hrvatske. Abroad, this work was published in Hrvatska revija in Croatian, and in Journal of Croatian Studies in English.