Watson was educated at Aberdeen Grammar School, Aberdeen University and the University of Cambridge (Peterhouse), where his doctoral thesis was on the poetry of Hugh MacDiarmid. He was later to write a critical study of MacDiarmid, whom he met and befriended as a student. Watson later taught at the University of Victoria in Canada, before coming back to Scotland and joining the University of Stirling.
He has written and lectured widely on Scottish literature and cultural identity, and served as General Editor of the Canongate Classics reprint series since the start of the project in 1987. He is a Fellow of the Royal Society of Edinburgh and is currently the co-editor (with Linda Dryden) of The Journal of Stevenson Studies.
He has published two main volumes of verse over the years, and has featured in numerous periodicals and anthologies. After an early pamphlet he published his debut work True History on the Walls in 1976, and this was followed by the Luath Press publication Into the Blue Wavelengths in 2004. Upon its publication it was lauded by Philip Hobsbaum, who labelled Watson as a "poet of introspection and retrospection".