Fellner was born in Moravia. Although untrained, his skills and knowledge, gained through experience, made him one of the most sought after architects of his day. In 1745 he settled in Tata, where he lived almost uninterrupted until his death. He played a major role in the development of towns in the area such as Pápa, Eger and Veszprém. Initially working for the Esterhazy family, his growing reputation lead to commissions from many others. His first major work was the Roman Catholic Tata Parish Church, which was initially built according to the plans of Franz Anton Pilgram in 1751, but most of it was erected according to Fellner's plans. Nevertheless, he was unable to finish the work and it was left up to Jozsef Grossmann to complete after Fellner's death. It was finally finished in 1783.
In 1764 Bishop Carl Eszterhazy put Fellner in charge of building works and planning in Eger, and this was to become one of the most important periods of his career. His first work for the city was the stairway section of the Bishop's palace and also its chapel in 1766. He also planned the bishop's palace in Veszprém. Fellner completed the Liceum building in Eger which was initially planned by Jozsef Gerl of Vienna. Fellner's last great work was the Parish Church at Pápa in 1773.
Fellner received a title in 1773. He died in Tata, and was buried in the crypt of Christchurch Roman Catholic Church which he had built. His apprentice Jozsef Grossmann finished his unfinished projects and also married his widow. In 1940 a statue was raised in his memory in front of the church in Tata.
1751-1776 Tata, Esterhazy castle
1751-1783 Tata, RC Parish church
1753 Tatabanya, garden city (kertvaros)
1754 Tata, Calvary Chapel
1754-1758 Cseklészi Cassle
1760 Penitent St John, RC Church
1761 Vértesboglár, Parish house
1762-1767 Mór, Lamberg Castle
1763-1769 Eger, Primate's Palace
1765-1780 Eger, Liceum
1765-1776 Veszprém, Bishop's Palace
1766 Eger, Bishop's palace stairwell and Chapel
1767-1770 Tata, Piarist House
1768 Vértesboglár, hotel
1770-1778 Veszprém, old people's home
1773-1775 Veszprém, seminary
1773 Pápa, Eszterházy castle interior remodelling
1774-1776 Eger, "Nagypréposti" Palace
1774-1783 Papa, Church
1775-1777 Nagyigmánd, RC Church
1777 Gyömrő, St John of Nepomuk RC Church
1777 Borsodszirák, RC Church
1777 Ászár, RC Church
1773 Pápa, RC Church
Numerous mills, e.g. at Tata and Miklos, the Nepomucenus, Jozsef, Cifra and Tovaros mills.
Also many country inns, parish churches, commercial buildings and houses were built.