His father was Raffaele Elia, the secretary of the Italian People's Party in Fano in the first post-war period and senator of Christian Democracy in the first two legislatures of the Republic.

He was secretary of the Group of Italian Parliamentarians to the Council of Europe and to the Common Assembly of the ECSC, and subsequently carried out managerial functions in the Assembly Secretariat, charged with formulating a constitution for Europe.

During the Turin years (1963–70) he formed around him a real school, made up of Gustavo Zagrebelsky, Alfonso Di Giovine, Mario Dogliani and Francesco Pizzetti.

He was elected judge of the Constitutional court by the Parliament on 30 April 1976, of which he became president in on 21 September 1981.

From 28 April 1993 to 10 May 1994 he served as Minister for Electoral and Institutional Reforms in the Ciampi Cabinet and from 19 April to 10 May 1994 was also Minister of Foreign Affairs ad interim, taking the place of Beniamino Andreatta who resigned as candidate for the European Parliament elections.