Gibson was educated at both the Hamilton Academy prep and senior schools and continued his studies at the University of Glasgow, where he was Cunninghame Gold Medallist in Mathematics, Donaldson Scholar in Chemistry, Major Young Bursar in Arts and Law, Metcalfe Bursar in Science, and Stewart Bursar and Prizeman in Law. He received degrees of M.A., B.Sc. and LL.B., all at the University of Glasgow. He was elected Secretary of the Glasgow University Students' Representative Council in 1909, and President in 1910.