How deep do Saturn's zonal winds penetrate below the cloud level has been a decades-long question, with important implications not only for the atmospheric dynamics but also for the interior density structure, composition, magnetic field, and core mass. The Cassini Grand Finale gravity experiment enables answering this question for the first time, with the premise that the planet's gravity harmonics are affected not only by the rigid body density structure but also by its flow field. Using a wide range of rigid body interior models and an adjoint based optimization for the flow field using thermal wind balance, we calculate the flow structure below the cloud level and its depth. We find that with a wind profile, largely consistent with the observed winds, when extended to a depth of around 8,800 km, all the gravity harmonics measured by Cassini are explained. This solution is in agreement with considerations of angular momentum conservation and is consistent with magnetohydrodynamics constraints.