Long-term deformation of the Earth’s surface inferred from Global Navigation Satellite Systems (GNSS) station position time series plays a central role in high-precision geodetic and geophysical applications, such as terrestrial reference frame realization, crustal deformation and strain rate estimation, or vertical land motion estimates for improved sea level change assessment. GNSS station position time series contain stochastic variations, often referred to as noise, that exhibit spatial correlations over distances of thousands of kilometers. The impact of these spatial correlations on the uncertainty of longterm station velocity estimates, however, remains poorly modeled and is therefore largely neglected. To address this limitation, we build on recent advances in the characterization and modeling of the spatio-temporal correlations of the noise in GNSS station position time series. We develop a multi-scale spatio-temporal noise correlation model and use it to derive the full covariance matrix of errors in a global station velocity field. Our results show that the spatio-temporally correlated noise induces significant and non-trivial correlations across station velocity errors, which depend not only on the distance between stations but also on the temporal overlap of the station position time series. Accounting for these spatial correlations could significantly improve the detection and uncertainty assessment of subtle long-term deformation signals. Plain Language Summary Position time series of Global Navigation Satellite Systems (GNSS) stations provide essential information about the long-term deformation of the Earth’s surface. However, the detection of subtle long-term deformation signals is limited by the presence of time-correlated noise in GNSS station position time series. Part of this noise has a largescale spatial structure, meaning that stations separated by large distances can experience similar noise patterns. This is usually ignored when estimating long-term deformation rates and their associated uncertainties. In this study, we describe how to model and account for spatially correlated noise in GNSS station position time series. This leads to more realistic uncertainty estimates for GNSS-derived long-term deformation and can benefit a variety of high-precision geodetic and geophysical applications.