Born in London in 1617, Wright trained in Edinburgh with the Scot George Jamesone. When civil war broke out, Wright went to Rome, joining the artists Academy there in 1648 (the only British artist so to do). In Rome he accumulated a collection of art works and books, later working in the Netherlands as an antiquary for Archduke Leopold Wilhelm of Austria. Returning to London in 1656, Wright was employed by both Royalists and Parliamentarians. After the Restoration in 1660, Wright painted Charles II – who appointed him his Picture Drawer in 1673 – and other members of the royal family. Little is known of his workshop or presumed assistants.
Wright was a Catholic, like many of his sitters, including ONeill. When, following the Popish Plot, Catholics were exiled from London, Wright travelled to Ireland in 1679, where he worked for at least four years. After Charles IIs death in 1685, the patronage of James II enabled Wright to accompany a 1686 embassy to Pope Innocent XI in Rome. Wright was buried at St Martin-in-the-Fields in 1694.