Hamilton came from a Scottish family which had emigrated to the Netherlands. By 1698 he had arrived in Vienna with his brother Philipp Ferdinand.

Like their father James, the brothers had specialised in animal and still life painting and were accepted as imperial chamber painters in the service of the Viennese court. Moreover, Johann Georg executed numerous commissions for the Liechtenstein and Schwarzenberg princely houses, addressing hunting and horse breeding themes as was deemed appropriate in art for the aristocracy.