Rossides was born in Lemesos in 1895. He studied Law in London, returning to Cyprus after graduation. During the uprising and protests of October 1931, he was arrested by the colonial authorities and confined to the village of Kythrea for the following two years.
He became the first permanent representative of Cyprus to the UN, serving between 1960 and 1979. From 1960 till 1973, Rossides also held the post of Ambassador to the United States, shuttling between Washington and New York to perform his duties. It was during this tenure that the intercommunal fighting of 1963-1964 and 1967 broke out, the coup d'etat against Makarios took place and the Turkish invasion of Cyprus (July 20, 1974) occurred.