Goldstein was born in Kingstree, South Carolina, the son of Fannie (Alpert) and Isadore E. Goldstein, who owned a clothing store. Goldstein received his BSci from Washington and Lee University in 1962, and his MD from Texas University's Southwestern Medical School in 1966. Upon completion of his residency, Goldstein moved to the National Institutes of Health (NIH) in Bethesda, Maryland, where he worked in biochemical genetics. In 1972, Goldstein relocated back to the Southwestern Medical Center, accepting a post as the head of the Division of Medical Genetics.

At the Southwestern Medical Center Goldstein collaborated extensively with Michael Brown, a fellow researcher at the center who had also worked at the NIH. From 1973 to 1985, Goldstein and Brown together published over one hundred major papers. They are both listed in Thomson Reuters’ index of highly cited authors. Frequently mentioned as a candidate for nationally-prominent positions in scientific administration, Goldstein, like his colleague Michael Brown, chose to continue hands-on research.

In 1988 Goldstein received a National Medal of Science in the field of molecular genetics, and in 2003 Goldstein and Brown won the Albany Medical Center Prize in Medicine and Biomedical Research in recognition for their further work in understanding cholesterol and also the discovery of an insulin-sensitive regulator, which potentially could be used to develop treatments for diabetes mellitus. Goldstein is a member of the U.S. National Academy of Sciences and the Institute of Medicine and he was elected a Foreign Member of the Royal Society (ForMemRS) in 1991.

In 1993, their postdoctoral trainees, Wang Xiaodong and Michael Briggs, purified the Sterol Regulatory Element-Binding Proteins (SREBPs), a family of membrane-bound transcription factors. Since 1993, Goldstein, Brown, and their colleagues have described the unexpectedly complex machinery that proteolytically releases the SREBPs from membranes, thus allowing their migration to the nucleus where they activate all the genes involved in the synthesis of cholesterol and fatty acids. The machinery for generating active SREBPs is tightly regulated by a negative feedback mechanism, which explains how cells maintain the necessary levels of fats and cholesterol in the face of varying environmental circumstances.

Goldstein was appointed as Chairman of the Albert Lasker Medical Research Awards jury in 1995, and was a recipient of the award ten years earlier. Since 2000, Goldstein has authored a series of essays on the deep relationship between art and science that appear in the annual Nature Medicine supplement that accompanies the Lasker Awards.

Since 2000, Goldstein has authored a series of essays considering science as a creative pursuit, and explores the links between the art and science. The essays appear in the journal Nature Medicine, and coincide with the annual announcement of the Lasker Awards, with which Goldstein is affiliated in the capacity of jury chairman.

Goldstein is Chair, Molecular Genetics at University of Texas Southwestern Medical Center. Together, Goldstein and Brown lead a research team that typically includes a dozen doctoral and postdoctoral trainees. They have trained over 145 graduate students and postdoctoral fellows, and five of their former postdoctoral fellows (Thomas C. Südhof, Wang Xiaodong, Helen H. Hobbs, David W. Russell, and Monty Krieger) have been elected to the U.S. National Academy of Sciences. Former postdoctoral fellow Thomas Südhof received the 2013 Nobel Prize in Medicine or Physiology and Helen H. Hobbs received the 2015 Breakthrough Prize in Life Sciences.

Among his professional activities, Goldstein is a member of the Board of Trustees of The Howard Hughes Medical Institute and of The Rockefeller University, where he was elected as a Life Trustee in 2015. He also serves as Chairman of the Board of Scientific Counselors of the Broad Institute, and is a member of the Board of Directors of Regeneron Pharmaceuticals, Inc. He previously served on The Board of Scientific Governors of the Scripps Research Institute, a nonprofit institute that conducts biomedical research.