Robust estimation of ground motions generated by scenario earthquakes is critical for many engineering applications. We leverage recent advances in generative adversarial networks (GANs) to develop a new framework for synthesizing earthquake acceleration time histories. Our approach extends the Wasserstein GAN formulation to allow for the generation of ground motions conditioned on a set of continuous physical variables. Our model is trained to approximate the intrinsic probability distribution of a massive set of strong‐motion recordings from Japan. We show that the trained generator model can synthesize realistic three‐component accelerograms conditioned on magnitude, distance, and . Our model captures most of the relevant statistical features of the acceleration spectra and waveform envelopes. The output seismograms display clear P‐ and S‐wave arrivals with the appropriate energy content and relative onset timing. The synthesized peak ground acceleration estimates are also consistent with observations. We develop a set of metrics that allow us to assess the training process’s stability and to tune model hyperparameters. We further show that the trained generator network can interpolate to conditions in which no earthquake ground‐motion recordings exist. Our approach allows for the on‐demand synthesis of accelerograms for engineering purposes.