Veevers is the son of George Stanley Veevers and Dulcie Annie (née James) and attended Newington College (1944-1947). In 1946 he won the Wigram Allen Scholarship, endowed by Sir George Wigram Allen, for General Proficiency. At the end of 1947 Veevers was named Dux of the College and received the Schofield Scholarship and Halse Rogers Prize. He went up to the University of Sydney and graduated as a Bachelor of Science in 1952 and a Master of Science in 1954.
Veevers was a cadet geologist at the Bureau of Mineral Resources, Geology and Geophysics, Canberra, (1948-1951), rising to geologist (1952-1960) and senior geologist 1961-1967. In 1968, he was appointed as a senior lecturer at Macquarie University and has since been an Associate Professor, Professor and Adjunct Professor of the Department of Earth and Planetary Sciences. He was awarded his PhD in 1956 from Imperial College London.
- Veevers crater - Named in his honour (1975)
- S W Carey Medal - Geological Society of Australia (1992)
- Centenary Medal - For service to Australian society and science in earth history (2001)
- Encyclopedia of Australian Science Retrieved 20 June 2012
- M J Banks Family Tree Retrieved 20 June 2012
- Newington College Register of Past Students 1863-1998 (Syd, 1999) pp 204
- Newington College Register of Past Students 1863-1998 (Syd, 1999) Part 2 - The Lists
- "Alumni Sidneienses". University of Sydney. Retrieved 20 June 2012.
- Macquarie University On-line DirectoryRetrieved 20 June 2012
- National Library of Australia CatalogueRetrieved 20 June 2012
- Geological Society of Australia S W Carey MedalRetrieved 20 June 2012
- It's an Honour Retrieved 20 June 2012
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