Magnetic skyrmions are localized chiral spin textures, which offer great promise to store and process information at the nanoscale. In the presence of asymmetric exchange interactions, their chirality, which governs their dynamics, is generally considered as an intrinsic parameter set during the sample deposition. In this work, we experimentally demonstrate that a gate voltage can control this key parameter. We probe the chirality of skyrmions and chiral domain walls by observing the direction of their current-induced motion and show that a gate voltage can reverse it. This local and dynamical reversal of the chirality is due to a sign inversion of the interfacial Dzyaloshinskii-Moriya interaction that we attribute to ionic migration of oxygen under gate voltage. Micromagnetic simulations show that the chirality reversal is a continuous transformation, in which the skyrmion is conserved. This control of chirality with 2–3 V gate voltage can be used for skyrmion-based logic devices, yielding new functionalities.