Wickramasinghe studied at Royal College, Colombo, the University of Ceylon (where he graduated in 1960 with a BSc First Class Honours in mathematics), and at Trinity College and Jesus College, Cambridge, where he obtained his PhD and ScD degrees. Following his education, Wickramasinghe was a Fellow of Jesus College, Cambridge from 1963 to 1973, until he became professor of applied mathematics and astronomy at University College Cardiff. Wickramasinghe was a consultant and advisor to the President of Sri Lanka from 1982 to 1984, and played a key role in founding the Institute of Fundamental Studies in Sri Lanka.