Born in Tunis, Tunisia as a French citizen, Donabédian is of Armenian origin. He studied Russian and Armenian, Armenology and history of medieval art at Provence University (1970–74), Yerevan State University, Yerevan Polytechnic Institute, the Academy of Fine Arts of Leningrad (1975–80), Paris XIII-Nanterre University (1980–85), and Montpellier III University (2002–04).

Between 1992 and 2006, he was employed by the French Ministry of Foreign Affairs as a culture counselor in Eastern Europe, including in Armenia (1992–96). Between 2006 and 2020, he was researcher at the Laboratoire d’Archéologie Médiévale et Moderne en Méditerranée (LA3M, Aix-en-Provence), and Associate Professor Emeritus of Armenian Studies and Medieval Art at Aix-Marseille University (AMU).He headed the Armenian-French archaeological mission to the 4th–6th-century church Yereruyk from 2009 to 2016.