After starting his career with FK Sutjeska Nikšić, he also played with FK Vojvodina and FK Budućnost Podgorica in the First League of FR Yugoslavia, before moving abroad, first to Austria, in 1998, to play with SKN St. Pölten, and next, in Greece, where he played with Aris Thessaloniki F.C. and AO Kavala, before moving to Hungary, to play with Debreceni VSC, before returning home, to finish his career with FK Lovćen Cetinje, in 2003.
Born in Nikšić (SR Montenegro, SFR Yugoslavia), he started his career in 1993 by playing with the local club FK Sutjeska Nikšić where in 7 seasons he made over 250 league appearances and scored over 30 goals.
Born in Višegrad, Čelebić started playing football for the youth side of FK Sutjeska Niksić.
He represented a number of domestic clubs, having played with all of them, beside Second League FK Radnički Pirot, in the Yugoslav First League, namely, FK Željezničar Sarajevo, FK Vojvodina, FK Sarajevo, NK Olimpija Ljubljana, NK Dinamo Zagreb and FK Sutjeska Nikšić.