After a successful sporting career in the former Yugoslavia which he began in the Adriatic city of Zadar in 1965, Cosic continued playing basketball in the United States for the University of Brigham Young, where he was proclaimed the best European player. He was the first European to be invited to play in the NBA league.
After Croatia gained independence, he worked at the Croatian Embassy in Washington.
He died at the age of 47 of a serious illness in Baltimore on 25 May 1995.