Amerasinghe joined the Ceylon Civil Service in 1937, starting a career that would span 44 years. As a civil servant he was appointed Resident Manager of the Gal Oya Development Board in 1950. Two years later he was sent on his first overseas appointment as Counsellor of Embassy of Ceylon in Washington, D.C. from 1953 to 1955. From 1955–1957, he was the Controller of Establishments, General Treasury; 1958, he became the Controller of Finance, Supply and Cadre, General Treasury; and, in the same year, was appointed as the Permanent Secretary to the Ministry of Nationalized Services and Road Transport, as well as Chairman of the Port Corporation. In 1961, Amerasinghe became Secretary to the Treasury and Permanent Secretary to the Minister of Finance, holding that post until 1963, while also serving as Official Member of the Monetary Board of the Central Bank and Alternate Governor for Ceylon in the International Bank for Reconstruction and Development. In 1963, he was appointed Ceylon High Commissioner to India, while serving concurrently as Ambassador to Nepal and Afghanistan, posts he held until moving to the United Nations in 1967.
United Nations
Amerasinghe was appointed Ceylon's Permanent Representative to the UN in 1967, a post he would hold until 1980. At the UN he held several key positions. These included Chairmanship of the United Nations Ad Hoc Committee on the Peaceful Uses of the Sea-Bed and the Ocean Floorbeyond the Limits of National Jurisdiction, President of the United Nations Conference on the Law of the Sea and chairman United Nations Sea-Bed Committee. Amerasinghe was also the Chairman of the Ad Hoc Committee on the Indian Ocean, which Sri Lanka proposed be designated as "zone of peace". He has chaired that Committee since it was created in 1973. Also, since its creation in 1969, he has been Chairman of the Special Committee to Investigate Israeli Practices Affecting the Human Rights of the Population of the Occupied Territories. In 1976 he became the President of the United NationsGeneral Assembly Thirty-first session of the general assembly. While serving as Permanent Representative, he held concurrent accreditation as Sri Lanka's Ambassador to Brazil. He was re-elected chairman of the Conference on the Law of the Sea in 1980, after he had left Sri Lanka's delegation to the United Nations. The Economist styled him the two million dollar chairman, because that's what the ten-day conference cost.
Death
He died on 4 December 1980 in New York, USA. For his services for the Law of the Sea, a fellowship in his name has been created by the UN.