Foster was the son of Johann Reinhold Foster. He showed a precocious intellectual ability and was educated in natural history by his father. He was enrolled as a pupil at the Warrington Academy, where his father taught French and German. When approached to join Cook’s Resolution, after Bank’s scientific party had withdrawn, Johann insisted that his son should travel with him as his natural-history draughtsman. George completed two volumes of drawings of plants containing 361 item on the voyage. These drawings the Fosters sold to Banks in August 1776.