Nagendra Singh was born into the RajputSisodia royal family of Dungarpur State in India as the third son of Maharaja Sri Sir Bijaya Singh and Maharani Devendra Kunwar Sahiba. He joined the Indian Civil Service and served as Regional Commissioner for the Eastern States, a member of the Constituent Assembly of India, joint secretary for India's Defense Ministry, Director-General of Transport, and special secretary in the Ministry of Information and Broadcasting.
Between 1966 and 1972 Singh was secretary to the President of India, then from 1 October 1972 to 6 February 1973 he was Chief Election Commissioner of India. In 1966, 1969, and 1975, he was appointed as a representative of India in the United Nations Assembly and served on the United Nations International Law Commission on a part-time basis from 1967 to 1972. He was also elected as secretary of the International Bar Association. In 1973, he moved to The Hague to become a judge of the International Court of Justice and was its president between February 1985 and February 1988, when he retired. He continued to live at the Hague and died there in December 1988.