Goldblum ble født i West Homestead nær Pittsburgh i Pennsylvania. Han var sønnen til Shirley, som var programleder for et radioprogram, og Harold Goldblum, som var lege. Han har en søster, Pamela, og en eldre bror, Lee. En annen bror, Rick, levde bare til han ble 23. Familien var jødisk og tilhørte en ortodokssynagoge. Goldblum flyttet til New York City i en alder av sytten år for å bli skuespiller.[9]
^abItzkoff, Dave (12. september 2014). «Playing Piano, and Blaming Woody Allen». The New York Times (på engelsk). ISSN0362-4331. Besøkt 27. oktober 2019. «Peter plays trumpet. So he would come over to my house, and the two of us would play a little bit. And then he did a Woody Allen movie [“Mighty Aphrodite”] and got to talking to Woody about us playing. Woody says: “You should do what I do, have a weekly gig, and you’ll get better. And it’ll be fun.” When Peter came back to L.A., we started to play out and about. And we got other musicians. In the years since, Peter’s living all over the world, but I’ve maintained this group. It’s Woody Allen’s fault, in a way.»
^«Jeff Goldblum's sneaky Billboard number one jazz album». RTE (på engelsk). 19. desember 2018. Besøkt 27. oktober 2019. «Actor Jeff Goldblum recently managed a number one jazz album, somewhat on the quiet in the US Billboard charts and his long-standing weekly gig in LA continues apace. "If I’m not out of town doing something, I’m there every week," the actor and piano player said of his residency with the Mildred Snitzer Orchestra at LA club Rockwell.»