Born in 1957 in Sevan.
Graduated from the Directing department of the Yerevan State Institute of Fine Arts. That same year, famous director Henrik Malyan invited Hakobyan to join the Studio by Studio Theatre (now, the Henrik Malyan Film Actor Studio) establishment. In 1991, Davit Hakobyan founded the "Triangle" theatre studio.
In 2006, Hakobyan was invited to Beirut to lead its two Armenian theater companies. The same year, he led the Yerevan State Chamber Music Theater.
He currently teaches at the Yerevan State Institure of Theatre and Cinema and the Mair Ator of Holy Etchmiadzin Gevorgyan Seminary.
Hakobyan was twice awarded the "Artavazd" prize of Armenia's Union of Theater Workers as Best Actor.