David Smith was born in South Wales on 21 May 1930. He was educated at Colston's School, Bristol, and at St. Paul's School, London, and then studied at The Queen's College, Oxford, where he was awarded the degrees of B.A. (first class honours in Botany), 1951, and Ph.D., 1954. After National Service, his academic career continued with a research fellowship at Queen's and he was Harkness Visiting Fellow at the University of California, Berkeley. Smith was back in Oxford in 1960, this time holding a University Lectureship in the Department of Agricultural Science, as well as an appointment as Royal Society Senior Research Fellow, then Tutorial Fellow and Admissions Tutor at Wadham College. In 1975, he became a Fellow of the Royal Society.

Smith then held the Melville Wills Chair of Botany at the University of Bristol, and in 1980 he became Professor of Rural Economy at the University of Oxford and Head of the Department of Agricultural Science. In 1986 he was knighted, and in 1987 he was appointed Principal of Edinburgh University in succession to John Harrison Burnett.

The published work of Sir David Smith centres on the biology of symbiosis and was initially concerned with associations between algae and fungi, and latterly with a variety of associations between algae and animals. With A. Douglas he publishedThe biology of symbiosis(1987).

During his period as Principal at Edinburgh, the University was confronted by challenges in the area of teaching (staff-student ratios), in research (assessments), and in financial policy, but through the resourceful leadeship that Smith provided, the University had been able to strengthen these areas again by the time that he retired in 1994.

Sir David Smith's portrait was painted by Scottish painter and printmaker Dame Elizabeth Blackadder (b. 1931) and it was unveiled on 21 March 1994.

From April 1994 to 2000, Sir David Smith was President of Wolfson College, Oxford.