The young Hungarian conductor is one of the most talented representatives of his generation, he took his diploma in percussion instruments and conducting with honors. In 1993 he founded the Danubia Youth Orchestra, of which he is still artistic director. In 1995 he became assistant conductor of the Budapest Festival Orchestra with a Leo Weiner scholarship. In 1998 he won first prize at the 9th International Conducting Competition of Hungarian Television, and also won the prize of the audience and the George Solti special prize. At the Athens Dimitris Mitropoulos International Conducting Competition he won a special prize and the grand prize of the Chromaton orchestra that participated in the event. In 2003 Domonkos Héja was awarded a Liszt Prize. He regularly receives invitations from leading Hungarian symphony orchestras, and is a frequent guest with numerous foreign ensembles including the Tokyo City Philharmonic Orchestra.

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Il quotidiano tedesco Der Tagessspeigel in occasione di un suo concerto con la Danubia Orchestra a Berlino nel 2000  ha scritto di lui "è senza dubbio un grande talento che presto raggiungerà la fama dei suoi famosi compatrioti Solti, Reiner, Szell e Ormandy"