Scott was born in Glasgow, Scotland. During World War II he served in the Royal Army in Britain and Nigeria. After the war he received an M.A. with Honours in English Literature and a Ph.D. from the University of Edinburgh. His first poems were published in 1941. Scott received an Atlantic Award for Literature in 1950 and traveled in France, Italy, and Sicily. During his travels he became interested in Scots literature as his own neglected native dialect, which shaped the direction of his work for the rest of his life.
He settled in Edinburgh and in 1953 married Heather Fretwell.