He studied Classics at University College, Oxford, taking a break midway for National Service in the Navy (HMS Hornet, 1956–57), and Law at the University of Edinburgh.
Edward was called to the Bar in 1962 and appointed Queen's Counsel in 1974. He subsequently served as Clerk and then Treasurer of the Faculty, and represented the Faculty at the Consultative Committee of the Bars and Law Societies of the European Community, of which he served as President between 1978–80. He was Salvesen Professor of European Institutions and Director of the Europa Institute at the School of Law of the University of Edinburgh from 1985 to 1989, during which time he served on three occasions as Specialist Adviser to the House of Lords Select Committee on the European Communities.
Edward was a Director of The Harris Tweed Authority from 1984–89. In 1989, he was appointed one of the inaugural Judges of the newly created European Court of First Instance, and in 1992 was appointed Judge of the , a position from which he retired in 2004. "A True European", a collection of essays for Sir David Edward, was published on his retirement, including "Tales from the Tartan Chambers".
Edward sat as a temporary judge of the Court of Session in Scotland, hearing civil appeals, until 2009. He is the Chairman of the Carnegie Trust for the Universities of Scotland and was Chair of the Scottish Council of Independent Schools from 2005 to 2010. He is an Honorary Fellow of University College, Oxford and an Honorary Bencher of Gray's Inn.
He is Professor Emeritus of the School of Law of the University of Edinburgh, and Chairman of its Europa Institute. In 2011, He was appointed as the Honorary President of the Scottish Arbitration Centre. Edward published an influential analysis of the position in European Union law if there were a vote in favour of Scottish independence in the Scottish independence referendum, 2014 as well as an opinion on Scotland's position in the European Union in a 2013/14 memorial to Alan Rodger, Baron Rodger of Earlsferry.
[Faculty of Advocates]
Edward is a Member of the Panel of Arbitrators, International Centre for Settlement of Investment Disputes. Edward was a member of the Commission on Scottish Devolution chaired by Professor Sir Kenneth Calman, Chancellor of the University of Glasgow. He was a member of the UK Commission on a Bill of Rights, 2011–12.