Daya Reddy was born in Port Elizabeth, South Africa. He obtained his BSc in civil engineering from the University of Cape Town in 1973, and PhD from the University of Cambridge in 1977. He has been an academic staff member at the University of Cape Town since 1979, and served as dean of the Faculty of Science over the period 1999 - 2005. Reddy currently holds the South African Research Chair in Computational Mechanics, in the Department of Mathematics and Applied Mathematics.

His research is concerned with the mathematical analysis and computational solution of problems arising in the mechanics of solids and fluids. Reddy is a founder member of the Academy of Science of South Africa (ASSAf), and was elected ASSAf President in October 2012. He is also a fellow of the South African Academy of Engineering, of the African Academy of Sciences, of The World Academy of Sciences (TWAS), and of the International Association of Computational Mechanics. He is president-elect of the International Council for Science.