Ground‐motion time series are essential input data in seismic analysis and performance assessment of the built environment. Because instruments to record free‐field ground motions are generally sparse, methods are needed to estimate motions at locations with no available ground‐motion recording instrumentation. In this study, given a set of observed motions, ground‐motion time series at target sites are constructed using a Gaussian process regression (GPR) approach, which treats the real and imaginary parts of the Fourier spectrum as random Gaussian variables. Model training, verification, and applicability studies are carried out using the physics‐based simulated ground motions of the 1906 7.9 San Francisco earthquake and 7.0 Hayward fault scenario earthquake in northern California. The method’s performance is further evaluated using the 2019 7.1 Ridgecrest earthquake ground motions recorded by the Community Seismic Network stations located in southern California. These evaluations indicate that the trained GPR model is able to adequately estimate the ground‐motion time series for frequency ranges that are pertinent for most earthquake engineering applications. The trained GPR model exhibits proper performance in predicting the long‐period content of the ground motions as well as directivity pulses.