The depth to which Jupiter’s observed east–west jet streams extend has been a long-standing question1,2. Resolving this puzzle has been a primary goal for the Juno spacecraft3,4, which has been in orbit around the gas giant since July 2016. Juno’s gravitational measurements have revealed that Jupiter’s gravitational field is north–south asymmetric5, which is a signature of the planet’s atmospheric and interior flows6. Here we report that the measured odd gravitational harmonics J3, J5, J7 and J9 indicate that the observed jet streams, as they appear at the cloud level, extend down to depths of thousands of kilometres beneath the cloud level, probably to the region of magnetic dissipation at a depth of about 3,000 kilometres7,8. By inverting the measured gravity values into a wind field9, we calculate the most likely vertical profile of the deep atmospheric and interior flow, and the latitudinal dependence of its depth. Furthermore, the even gravity harmonics J8 and J10 resulting from this flow profile also match the measurements, when taking into account the contribution of the interior structure10. These results indicate that the mass of the dynamical atmosphere is about one per cent of Jupiter’s total mass.