The age of Jupiter, the largest planet in our Solar System, is still unknown. Gas-giant planet formation likely involved the growth of large solid cores, followed by the accumulation of gas onto these cores. Thus, the gas-giant cores must have formed before dissipation of the solar nebula, which likely occurred within less than 10 My after Solar System formation. Although such rapid accretion of the gas-giant cores has successfully been modeled, until now it has not been possible to date their formation. Here, using molybdenum and tungsten isotope measurements on iron meteorites, we demonstrate that meteorites derive from two genetically distinct nebular reservoirs that coexisted and remained spatially separated between ∼1 My and ∼3–4 My after Solar System formation. The most plausible mechanism for this efficient separation is the formation of Jupiter, opening a gap in the disk and preventing the exchange of material between the two reservoirs. As such, our results indicate that Jupiter’s core grew to ∼20 Earth masses within <1 My, followed by a more protracted growth to ∼50 Earth masses until at least ∼3–4 My after Solar System formation. Thus, Jupiter is the oldest planet of the Solar System, and its solid core formed well before the solar nebula gas dissipated, consistent with the core accretion model for giant planet formation.