Moffat was born in Dunfermline in 1943 and studied painting at Edinburgh College of Art (1960-1964). He became Chairman of the New 57 Gallery in Edinburgh in 1968, a position he held until 1978. In 1979 he joined the staff of Glasgow School of Art where he was Head of the Painting Department from 1992 until his retirement in 2005. His paintings are represented in many collections in the UK and in the Yale Centre for British Art, USA, and the Pushkin Museum in Moscow. He was awarded an OBE for his services to the arts in 2006.