Burgin was born in Sheffield in England. He studied art at the Royal College of Art before going to the United States to study at Yale University.
Burgin first came to attention as a conceptual artist. He has worked with in photography and film, calling painting "the anachronistic daubing of woven fabrics with coloured mud".
Burgin has taught at Goldsmiths College, the University of California, Santa Cruz and the European Graduate School in Saas-Fee, Switzerland.
In 1986, Burgin was nominated for the Turner Prize.