Hudson was a portrait painter, born in Devon. He trained under the successful portrait painter Jonathan Richardson, later marrying his daughter. He had many artistic friends including William Hogarth, Allan Ramsay and Francis Hayman. Hudson retained these connections, travelling to France, Holland and Flanders with Hogarth and Hayman in 1748 and to Italy with the sculptor Louis-François Roubiliac in 1752. Having established his own portrait-painting practice, Hudson became increasingly fashionable. As the number of commissions grew, he employed drapery painters to assist him. His many pupils included Joshua Reynolds and Joseph Wright of Derby.