Tennekoon started his legal practice in the unofficial bar in Kegalle and was appointed a Temporary Additional Crown Counsel on 1 October 1946 in the Attorney-General's Department. From 14 March 1949 to 5 March 1951, he was seconded to serve as the Secretary to the Kandyan Peasantry Commission. In September 1949 he was appointed Crown Counsel; in November 1955, he was appointed Acting Senior Crown Counsel and in May 1956 confirmed as Senior Crown Counsel. Between April 1957 and June 1961, he served as Acting Deputy Solicitor General. Although he specialized in civil law, he attended Columbia University on a senior fellowship in constitutional law from the Asia Foundation between September 1961 to March 1962 and on his return joined the Attorney-General's prosecution team in the 1962 coup d'état attempt. Appointed Solicitor General of Ceylon in 1964 he played a key role formulating the Sirima–Shastri Pact working as an advisor to the government on aspects of international law relating to the nationality problems of Indian Tamils of Sri Lanka in collaboration with Sir Humphrey Waldock. In 1965 he took silks as a Queen's Counsel. In 1967, he was appointed to the Supreme Court of Ceylon as a Puisne Justice. He was the first Kandyan to serve in the Supreme Court bench, serving from 8 February 1967 to 1 July 1970.[3][4]
In July 1970, he was appointed Attorney General. During his term, he created the controversial Criminal Justice Commission to prosecute a large number of suspects of the 1971 JVP insurrection, which was later extended to prosecute exchange control violators. Reaching the public service retirement age of 60, he was appointed a Judge of the Court of Appeal of Sri Lanka in August 1973 and served till 31 December 1973. On 1 January 1974 he was appointed Chief Justice, succeeding Gardiye Punchihewage Amaraseela Silva and served till his retirement on 8 September 1977.