Goldstein attended Washington and Lee Universty, Virginia, and the University of Texas Southwestern Medical School, where he gained his MD in 1966. For two years he worked at Massachusetts General Hospital, Boston. In 1968 he joined the National Institutes of Health as a clinical associate (1968–70). After a stint of research at the University of Washington, Seattle (1970–72), he joined the University of Texas Health Science Center in Dallas. In 1977 Goldstein was appointed professor of medicine and chairman of the Department of Molecular Genetics, and in 1985 he was made regental professor.

Goldstein's work has centered on the metabolism of cholesterol, fats, and other lipids in the body; much of it has been done in collaboration with his fellow biochemist and geneticist, Michael Brown (1941– ), whom Goldstein met when both were interns at Massachusetts General Hospital in 1966. Starting in the early 1970s, the pair began by studying how cells obtain their cholesterol from blood. Most of the blood's cholesterol is present in the form of low-density lipoproteins (LDLs) – minute particles comprising proteins, cholesterol, and other lipids. Working with cultures of skin cells, Goldstein and Brown discovered receptors on the cell surface that recognize the LDLs and bind them to the cell membrane. The LDL is subsequently enfolded by the cell membrane and taken into the cell, where its contents are metabolized (cholesterol, for instance, is a vital component of cell membranes).

They went on to show that there is a deficiency of LDL membrane receptors in individuals suffering from the inherited disorder knwon as familial hypercholesterolemia. Such persons have abnormally high levels of cholesterol in their blood and run a much greater risk of developing atherosclerosis – the narrowing of the arteries due to a build-up of fatty plaques on their inner surface. This in turn makes them much more prone to heart attacks and strokes. Goldstein and Brown were able to show that in this disorder the gene encoding the LDL receptors is defective, hence the number of such receptors is small and the sufferer's body cells are unable to remove LDLs from the bloodstream. The consequent high blood-cholesterol levels prompt scavenger white cells to remove the cholesterol, turning them into the plaque-forming cells thought to be responsible for atherosclerosis.

The work of the Goldstein and Brown has covered many other aspects of cholesterol metabolism, particularly how the cholesterol absorbed from the gut into the bloodstream is processed and repackaged by the liver, with the formation of high-density, very-low-density, and intermediate-density lipoproteins. They have not only revealed fundamental features of cellular metabolism but have shown ways in which people with elevated blood cholesterol may be treated, for instance by increasing the number of LDL receptors on their cells. This, in turn, may reduce their risk of heart attacks and strokes.

For his work on familial hypercholesterolemia and LDl receptors, Goldstein was awarded the 1985 Nobel Prize for physiology or medcine, which he shared with his long-time colleague, Brown.