He was born in Derby, the son of an attorney, who was afterwards town-clerk. Deciding to become a painter, he went to London in 1751 and for two years studied under Thomas Hudson, the master of Joshua Reynolds. After painting portraits for a while at Derby, he again placed himself for fifteen months under his former master. He then settled in Derby, and varied his work in portraiture by the production of the subjects seen under artificial light with which his name is chiefly associated, and by landscape painting.
He married in I773, and in the end of that year he visited Italy, where he remained till 1775. While at Naples he witnessed an eruption of Mount Vesuvius, which formed the subject of many of his subsequent pictures. On his return from Italy he established himself at Bath as a portrait-painter; but meeting with little encouragement he returned to Derby, where he spent the rest of his life.
He was a frequent contributor to the exhibitions of the Society of Artists, and to those of the Royal Academy, of which he was elected an associate in 1781 and a full member in 1784. He, however, declined the latter honour on account of a slight which he believed that he had received, and severed his official connection with the Academy, though he continued to contribute to the exhibitions from 1783 till 1794.
Wright's portraits are frequently defective in drawing, and without quality or variety of handling, while their flesh tints are often hard. He is seen at his best in his subjects of artificial light, of which the Orrery (1766), the property of the corporation of Derby, and the Air-pump (1768), in the National Gallery, are excellent examples. His Old Man and Death (1774) is also a striking and individual production. An exhibition of Wright's works was brought together at Derby in 1883, and twelve of his pictures were shown in the winter exhibition of the Royal Academy in 1886.