Antony Williams was born in St Asaph, Wales, June 1964 to Ernest Edward Williams, owner of a building contracting firm, and Eirlys Elizabeth Williams. He has one older sister, Rae. He grew up in a small village near Caerwys.
Williams attended Primary School in both Holywell and Nannerch until 1975. From the age of eleven, he attended Alun School where he received A-levels in mathematics, geography, and chemistry.
Williams earned his Bachelor of Science in chemistry from the University of Liverpool, in 1985, writing an undergraduate dissertation on "Spectroscopic Studies of Vitamin E Related Systems" where he applied both electron paramagnetic resonance (EPR) and Nuclear magnetic resonance spectroscopy (NMR) to the study of molecules similar in structure to Vitamin E.
Williams earned his Ph.D. in chemistry, funded by Royal Dutch Shell, from Royal Holloway, University of London in 1988 and wrote a thesis entitled "High pressure NMR and relaxation studies of alkyl chain systems". He won the Bourne Medal from the University of London for this work and developed a unifying theory for modeling NMR relaxation data to examine the molecular motions of alkyl chains. He also used the Cobalt-59 NMR chemical shift for cobalt (III) hexacyanide as both a temperature and pressure probe. During his PhD he developed an interest in personal computers and wrote software programs to fit NMR relaxation data.
Williams continued his work in spectroscopy at the National Research Council (Canada) using EPR spectroscopy to perform single-crystal studies of organometallics compounds.