Miller was the son of the artist Johann Sebastian Müller (1715- c.1790) (abbreviation in botany : J.S.Muell.). He was one of the artists who converted Sydney Parkinson's drawings from James Cook's first voyage into paintings. He accompanied Joseph Banks on his expedition to Iceland in 1772.
Miller published Cimelia Physica. Figures of rare and curious quadrupeds, birds, &c. together with several of the most elegant plants (1796) with text by George Shaw.