Stuart was born in Edinburgh and raised in St. Andrews, studying at Madras College. He completed a BSc and PhD in inorganic chemistry at the University of Edinburgh, working for the latter with Lesley Yellowlees and Alan Welch. He won a NATO Western European Fellowship to work with Odile Eisenstein at the Université de Paris-Sud in Orsay (1992-1994). After a further post-doctoral position at the Australian National University in Canberra he returned to Edinburgh in 1997 to take up a lectureship at Heriot-Watt University. He was promoted to Reader in 2006 and full Professor in 2009 and served as Head of the Institute of Chemical Sciences from 2010 to 2015. Stuart's research uses computational methods to model the structure and reactivity of transition metal systems in both solution and the solid state. He works in close collaboration with experimentalists and targets applications in catalysis. In 2019 he received the Royal Society of Chemistry's Ludwig Mond Award for his work exploring novel mechanisms of C–H and C–F activation and the organometallic chemistry of σ-alkane complexes in the solid state.