Kornberg was born in Brooklyn, New York, and graduated from the City College of New York in biology and chemistry in 1937. He then studied medicine at Rochester University, gaining his MD in 1941. He joined the National Institutes of Health, Bethesda, where from 1942 to 1953 he directed research on enzymes. During this period he helped elucidate the reactions leading to the formation of two important coenzymes, flavin adenine dinucleotide (FAD) and diphosphopyridine nucleotide (DPN; later renamed nicotinamide adenine dinucleotide – NAD).

From 1953 to 1959 Kornberg was professor of microbiology at Washington University. In 1956, while investigating the synthesis of coenzymes, he discovered an enzyme that catalyzes the formation of polynucleotides from nucleoside triphosphates. This enzyme, which he named DNA polymerase, can be used to synthesize short DNA molecules in a test tube, given the appropriate triphosphate bases and a DNA template. For the discovery and isolation of this enzyme, Kornberg was awarded the 1959 Nobel Prize for physiology or medicine, sharing the award with Severo Ochoa, who discovered the enzyme catalyzing the formation of RNA.

Kornberg was chairman of the biochemistry department at Stanford University from 1959 and his work there has contributed to the understanding of the synthesis of phospholipids and many reactions of the tricarboxylic acid, or Krebs, cycle.