The Kipferl (ancestor of the croissant) has been documented in Austria going back at least as far as the 13th century, in various shapes.
The “birth” of the croissant itself – that is, its adaptation from the plainer form of Kipferl, before its subsequent evolution (to a puff pastry) – can be dated with some precision to at latest 1839 (some say 1838), when an Austrian artillery officer, August Zang, founded a Viennese Bakery (“Boulangerie Viennoise”) at 92, rue de Richelieu in Paris.