Born to Glanville Peiris, diplomat who was the former Director-General External Affairs, Ceylon's Ambassador to West Germany and Myanmar and Lakshmi Chandrika Peiris.
In 2001, Wijesekara left the President Chandrika Kumaratunga's ruling Sri Lanka Freedom Party and joined United National Party along with few other senior ministers of the government such as S. B. Dissanayake and G. L. Peiris.