Goonesekere studied at Ladies' College, Colombo, and obtained arts and law degrees at the University of Peradeniya in 1961, graduating with First Class Honours.
She attended Harvard Law School as a Smith-Mundt Fulbright scholar, where she obtained her master’s degree in 1962.
In 1983 Goonesekere was appointed as Professor of Law at the Open University of Sri Lanka, the first woman to hold this position, and was subsequently appointed the Dean of the Faculty of Humanities and Social Sciences.
Prof. Goonesekere was awarded an honorary Doctorate of Letters from the Open University of Sri Lanka and an honorary Doctorate of Law by the University of Colombo, in recognition of her contributions to these institutions.
A prolific writer, Goonesekere was instrumental in the evolution of modern legal education in Sri Lanka.