Webber was the son of the Swiss sculptor Abraham Wäber. He trained in Berne with the landscape painter Johann Ludwig Aberli, and then from 1770 studied at the Académie Royale in Paris. He entered the Royal Academy Schools in London and exhibited there in 1776. His work impressed the botanist Dr Daniel Carl Solander, who recommended his employment as the official artist on Captain James Cook’s third voyage (1776-80). This expedition was planned to find a sea passage around the north of America. They sailed on the ‘Resolution’ and Webber made drawings throughout the voyage. They visited Tasmania, New Zealand, the South Pacific and the Sandwich Islands (Hawaii), and the Icy Cape. Webber witnessed Cook’s death. On his return to Britain, a number of his illustrations were engraved.