Gresse studied drawing under Gerard Scotin, the engraver, and was one of the first students to work in the gallery of casts founded by the Duke of Richmond.
Gresse lacked the industry and application necessary to succeed in the higher branches of his art, and as he inherited a sufficient income from his father, he did not exert his full powers.
In 1765 he became a member of the rival Incorporated Society of Artists, and exhibited with them for four years, chiefly miniatures.
Gresse died on 19 February 1794, in his fifty-third year, and was buried at St. Anne's, Soho.
He was a great collector of works of art, which were sold by auction shortly after his death, the sale occupying six days.