Vashegyi was born in Budapest on April 13, 1970. He began his musical career as an instrumentalist, studying violin, recorder, oboe, and harpsichord. When he was 16, he made his debut as a conductor, and he enrolled at the Franz Liszt Academy of Music at 18 as a conducting student. He worked there with Ervin Lukács and took master classes from John Eliot Gardiner and Helmuth Rilling before graduating in 1993. Vashegyi went on for studies in basso continuo in Dresden, Germany, with John Toll from 1994 to 1997 and with viol player Jaap ter Linden and Baroque violinist Simon Standage. He landed continuo spots in the Hungarian early music ensemble Concerto Armonico and in the Franz Liszt Chamber Orchestra. By that time, he had already founded his own early music groups; he assembled the Purcell Choir for a performance of Purcell's opera Dido and Aeneas and the Orfeo Orchestra the following year for one of Monteverdi's Orfeo. As his skills developed, these two groups took on more definite shapes and began to perform together frequently. In 1998, they made their recording debuts together on a recording of the St. Benedict Mass of Benedek Istvánffy and the Requiem of Joseph Martin Kraus. That recording appeared on the Hungaroton label, where Vashegyi recorded often in the 1990s and 2000s decades.
Vashegyi has become a prominent figure in Eastern Europe's early music scene, conducting not only his own groups but also such ensembles as Hungary's Capella Savaria. His ensembles are popular festival attractions, and the Orfeo Orchestra has often accompanied the Hungarian State Opera in Baroque and Classical-era opera productions. Vashegyi has also conducted modern symphony orchestras. He guest-conducted the Hungarian National Philharmonic Orchestra at the invitation of pianist Zoltán Kocsis in 2002 and has gone on to lead groups both inside and outside Hungary, including the Szeged Symphony Orchestra, the Hungarian Radio Symphony Orchestra, and the Prague Chamber Orchestra. He moved to the Glossa label in 2015 for a recording of Rameau's opera Les fêtes de Polymnie and made several recordings for that label. In the early 2020s, he also recorded for Accent, issuing a recording of Michael Haydn's oratorio Kaiser Constantin I: Feldzug und Sieg on that label in 2022. By that time, his catalog comprised more than 35 items, many containing music exposed by his own research. Vashegyi has won major Hungarian cultural prizes, and in 2022, he was made a Knight of the French Order of Arts and Letters. ~ James Manheim, Rovi