He was educated at Lancaster Royal Grammar School, King's College London (BSc Joint Hons, Zoology and Botany), Durham University (MSc Advanced Ecology) and the University of East Anglia (UEA) (PhD, 1980).
His PhD "Qualitative changes in the regulation of Sycamore aphid numbers" was supervised by Professor Tony Dixon.
He has been of Director of the Australian Nuclear Science and Technology Organisation (ANSTO), the Australian Centre for International Agricultural Research (ACIAR), the Cumbrian Rural Regeneration Company, the Bundanon Trust, University of Wollongong Global Enterprises, the General Sir John Monash Foundation and the Global Foundation.
During his academic career he was a board member of Universities UK and chair of UUK's International and European Policy Committee, and a board member of Higher Education Funding Council for England (HEFCE) and Chair of HEFCE's Research Committee, Chair of the 1994 Group of research-intensive universities and, during the COVID-19 pandemic, convener of NSW Vice-Chancellors Committee.
Wellings was appointed Commander of the Order of the British Empire (CBE) in the 2012 Birthday Honours for services to higher education.