Smith was born on August 23, 1931, and graduated from University Laboratory High School of Urbana, Illinois. He attended the University of Illinois at Urbana-Champaign, but in 1950 transferred to the University of California, Berkeley, where he earned his B.A. in Mathematics in 1952 He received his medical degree from Johns Hopkins University in 1956.
He later became a leading figure in the nascent field of genomics, when in 1995 he and a team at The Institute for Genomic Research sequenced the first bacterial genome, that of Haemophilus influenzae. H. influenza was the same organism in which Smith had discovered restriction enzymes in the late 1960s. He subsequently played a key role in the sequencing of many of the early genomes at The Institute for Genomic Research, and in the sequencing of the human genome at Celera Genomics, which he joined when it was founded in 1998.
He currently directs a team at the J. Craig Venter Institute that works towards creating a synthetic bacterium, Mycoplasma laboratorium. In 2003 the same group had synthetically assembled the genome of a virus, Phi X 174 bacteriophage.