Konjovic was born in Stanišić near the town of Sombor, Vojvodina, a region which was then part of Austro-Hungarian Empire.
After four years of studies he sailed in the Mediterranean and on the oceans serving as an Austro-Hungarian Navy navigation officer.
He got acquainted with aviation in 1911 and 1912 during his service in Pula, where he flew a seaplane built by engineer Josif Mikla.
After the armistice in 1918 Konjović handed over the Austro-Hungarian marine air fleet under the command of the Kingdom of Serbs, Croats and Slovenes and later was appointed the first head of the Naval Aviation of the new country, remaining in this position until 1923.
During World War II, when the Axis powers occupied Yugoslavia, Konjović was arrested and imprisoned in the Banjica concentration camp near Belgrade for a few years.