Foulds received a Bachelor of Medicine degree in 1946 and a Doctor of Medicine degree in 1958 from Glasgow University. In 1952, he earned his Doctor of Osteopathic Medicine degree from Royal College of Physicians & Royal College of Surgeons of England.
Foulds began his career as a registrar at Moorfields Eye Hospital in 1951. Two years later he took a position of a senior registrar at the University College Hospital of London and held it for five years. The same years Wallace was a research assistant at the Institute of Ophthalmology of London University.
He served as a consultant of ophthalmologist at Addenbrookes Hospital of Cambridge from 1958 to 1990. Also the same years Foulds was an honorary lecturer at Cambridge University, research fellow and senior lecturer in the Department of Experimental Ophthalmology at the Institute of Ophthalmology of London University. In 1964, Foulds was appointed to the Tennent Chair of Ophthalmology at the University of Glasgow to head a clinical department.
In 1990, he became an adviser in research at Singapore National Eye Centre and Singapore Eye Research Institute and a visiting professor at National University of Singapore. Ten years later Wallace was appointed a co-director at Singapore Eye Research Institute. In 2002, he held the position of a visiting professor in the Department of Ophthalmology at National University of Singapore.
Foulds is a member of the Royal Australian and New Zealand College of Opthalmologists, the Royal College of Ophthalmologists, College of Surgeons of South Africa, the Royal Society of Medicine, the Royal Colleges of Surgeons and The Medical & Dental Defence Union for Scotland.
On December 20, 1947 Wallace Foulds married Margaret Holmes Walls. They have 3 children.