Watson did his Ph.D. at the University of Glasgow, and worked in the UK, United States and Canada. He was a postdoctoral fellow under Jon Hougen in the Molecular Spectroscopy Group of Gerhard Herzberg at the National Research Council of Canada in Ottawa, Ontario from 1963 to 1965. He eventually joined the staff in the group in 1982 where he remained until retirement.
Watson published a number of papers in which he developed and applied molecular Hamiltonians to problems in spectroscopy. In 1968 Watson published Simplification of the molecular vibration-rotation Hamiltonian, in which he presented a practical framework for the quantum-mechanical description of molecular ro-vibrational dynamics within the Born-Oppenheimer approximation.