Govedarica was born on November 18, 1949, in Bačko Dobro Polje, SAP Vojvodina, SR Serbia.
His parents hail from Gacko in Bosnia and Herzegovina originally, from where they moved to Vojvodina after the end of World War II.
Blagoje moved with his parents, finishing school in Nikšić, before leaving for Belgrade to study archeology and Illyrology at the Faculty of Philosophy in Belgrade and eventually graduate in 1973, and receive his master's degree in 1980.
[1][2] In 1973, he started working at the Centar za balkanološka ispitivanja (Center for Balkanological Research) in Sarajevo, where he is direktor.
[3] He is also a scientific advisor (consultant) in the department for the archaeology, protection and preservation of cultural monuments.