Lederberg was born in Montclair, New Jersey, to a Jewish family, son of Esther Goldenbaum Schulman Lederberg and Rabbi Zvi Hirsch Lederberg, in 1925, and moved to Washington Heights, Manhattan as an infant. He had two younger brothers. Lederberg graduated from Stuyvesant High School in New York City at the age of 15 in 1941. After graduation, he was allowed lab space as part of the American Institute Science Laboratory, a forerunner of the Westinghouse Science Talent Search. He enrolled in Columbia University in 1941, majoring in zoology. Under the mentorship of Francis J. Ryan, he conducted biochemical and genetic studies on the bread mold Neurospora crassa. Intending to receive his MD and fulfill his military Service obligations, Lederberg worked as a hospital corpsman during 1943 in the clinical pathology laboratory at St. Albans Naval Hospital, where he examined sailors' blood and stool samples for malaria. He went on to receive his undergraduate degree in 1944.

Lederberg married fellow scientist Esther Miriam Zimmer in 1946; they divorced in 1966. He married Psychiatrist Marguerite Stein Kirsch in 1968. He was survived by Marguerite, their daughter, Anne Lederberg, and his stepson, David Kirsch.

Throughout his career, Lederberg was active as a scientific advisor to the U.S. government. Starting in 1950, he was a member of various panels of the Presidential Science Advisory Committee. In 1979, he became a member of the U.S. Defense Science Board and the chairman of President Jimmy Carter's President's Cancer Panel. In 1989, he received National Medal of Science for his contributions to the scientific world. In 1994, he headed the Department of Defense's Task Force on Persian Gulf War Health Effects, which investigated Gulf War Syndrome.

Joshua Lederberg and Norton Zinder showed in 1951 that genetic material could be transferred from one strain of the bacterium Salmonella typhimurium to another using viral material as an intermediary step. This process is called transduction. In 1956, M. Laurance Morse, Esther Lederberg and Joshua Lederberg also discovered specialized transduction. The research in specialized transduction focused upon lambda phage infection of E. coli. Transduction and specialized transduction explained how bacteria of different species could gain resistance to the same antibiotic very quickly.

During her time in Joshua Lederberg's laboratory, Esther Lederberg also discovered fertility factor F, later publishing with Joshua Lederberg and Luigi Luca Cavalli-Sforza. In 1956, the Society of Illinois Bacteriologists simultaneously awarded Joshua Lederberg and Esther Lederberg the Pasteur Medal, for "their outstanding contributions to the fields of microbiology and genetics".

In 1957, Joshua Lederberg founded the Department of Medical Genetics at the University of Wisconsin–Madison. He has held visiting professorship in Bacteriology at the University of California, Berkeley in summer 1950 and University of Melbourne (1957). Also in 1957, he was elected to the National Academy of Sciences.

In 1958, Joshua Lederberg received the Nobel Prize and moved to Stanford University, where he was the founder and chairman of the Department of Genetics. He collaborated with Frank Macfarlane Burnet to study viral antibodies. With the launching of Sputnik in 1957, Lederberg became concerned about the biological impact of space exploration. In a letter to the National Academies of Sciences, he outlined his concerns that extraterrestrial microbes might gain entry to Earth onboard spacecraft, causing catastrophic diseases. He also argued that, conversely, microbial contamination of manmade satellites and probes may obscure the search for extraterrestrial life. He advised quarantine for returning astronauts and equipment and sterilization of equipment prior to launch. Teaming up with Carl Sagan, his public advocacy for what he termed exobiology helped expand the role of biology in NASA.

In the 1960s, he collaborated with Edward Feigenbaum in Stanford's computer science department to develop DENDRAL.

In 1978, he became the President of Rockefeller University, until he stepped down in 1990 and became professor-emeritus of molecular genetics and informatics at Rockefeller University, reflecting his extensive research and publications in these disciplines.

Instead of returning to Columbia to finish his medical degree, Lederberg chose to accept an offer of an assistant professorship in genetics at the University of Wisconsin–Madison. His wife Esther Lederberg went with him to Wisconsin. She received her doctorate there in 1950.