Zach was born in Čelákovice, Bohemia into a wheelwright's family. In 1724 he moved to Prague and started working as violinist at St Gallus and at St Martín. According to Dlabacž, he studied organ under Bohuslav Matěj Černohorský.
He traveled through Europe and supported himself financially by performing and selling copies of his works, teaching, dedicating his compositions, and so on. He visited numerous courts and monasteries in Germany and Austria, stayed in Italy in 1767 and between 1771 and 1772, and may have worked as choirmaster at the Pairis Abbey in Alsace. He stayed several times at the Stams Abbey at Stams, Tyrol, where he may have had connections, and served as music teacher at the Jesuit school in Munich, for several brief periods of time. The last mentions of Zach in contemporary sources indicate that in January 1773 he was at the Wallerstein court, and according to the Frankfurt Kayserliche Reichs-Ober-Post-Amts-Zeitung of 5 June 1773 he died on a journey, at Ellwangen. Zach was buried in the local church of St Wolfgang.