The formation history of giant planets determines their primordial structure and consequent evolution. We simulate various formation paths of Jupiter to determine its primordial entropy, and find that a common outcome is for proto-Jupiter to have non-convective regions in its interior. We use planet formation models to calculate how the entropy and post-formation luminosity depend on model properties such as the solid accretion rate and opacity, and show that the gas accretion rate and its time evolution play a key role in determining the entropy profile. The predicted luminosity of Jupiter shortly after formation varies by a factor of 2–3 for different choices of model parameters. We find that entropy gradients inside Jupiter persist for ∼10 Myr after formation. We suggest that these gradients should be considered together with heavy-element composition gradients when modelling Jupiter’s evolution and internal structure.