He was the son of Gabriel II Tavernier, an engraver who moved from Antwerp to Paris in 1573. He had four siblings: Jean-Baptiste (who became a well-known writer and traveller), Gabriel III, Daniel, and Marie. He described his uncle, the elder Melchior Tavernier (1544-1641), who is otherwise obscure, as having introduced the art of engraving to Paris. He apprenticed with Thomas de Leu on 30 June 1609.
In 1618 Tavernier became an intaglio engraver and printer to the king (graveur et imprimeur en taille-douce du Roi) with an emphasis on maps. Abraham Bosse became his apprentice in 1621. Tavernier operated his shop in Paris at many locations but finally settled on the Isle du Palais, first on the rue de Harlay and later on the quai facing the quai de la Mégisserie [fr], where it was known as 'L'Espic d'Or' (1627-1635), then 'La Sphère Royalle' (1635 and later). In 1644 he sold his shop to Pierre Mariette (1596-1657), the grandfather of Jean Mariette.