SUMMARY We analyse Global Navigation Satellite System (GNSS) data from Svalbard to understand how uplift rates are controlled by the elastic and viscoelastic response of the solid Earth to changes in glacier mass on annual, interannual, decadal, centennial and millennial timescales. To reveal local patterns of deformation, we filter the GNSS time-series with an enhanced common-mode filtering technique where the non-tidal loading signal is incorporated. This technique reduces the estimated uncertainties for 5-yr time-series from 0.8 to 0.3 mm yr–1. Analysis of the GNSS data with different software–GAMIT, GipsyX, and GINS–produce consistent results that all indicate large temporal variations in uplift. For example, at the Ny-Ålesund GNSS station, uplift varies between 6 and 12 mm yr–1 for different 5-yr periods, and also shows a significant increase in the last 15 yr. We show that this increase is due to climate change-related ice mass loss in Svalbard. We constrain recent glacier retreat on Svalbard using a series of digital elevation models, and then correct the GNSS-derived uplift records for the elastic signal from these ice mass changes. The residual uplift signal is relatively constant, confirming the hypothesis that current ice mass changes exert a strong influence on GNSS observations. The relatively constant record of residual uplift can be used to constrain other geophysical signals such as the viscoelastic response of the solid Earth to ice loading during the Little Ice Age and the Last Glacial Period. We review uplift results from previous viscoelastic modelling studies and show that the residual signal cannot yet be fully explained. Our new uplift results thus motivate the need for new viscoelastic modelling of the glacial isostatic adjustment process in Svalbard.