Estimating mass changes of ice sheets or of the global ocean from satellite gravimetry strongly depends on the correction for the glacial isostatic adjustment (GIA) signal. However, geophysical GIA models are different and incompatible with observations, particularly in Antarctica. Regional inversions have resolved GIA over Antarctica without ensuring global consistency, while global inversions have been mostly constrained by a priori GIA patterns. For the first time, we set up a global inversion to simultaneously estimate ice sheet mass changes and GIA, where Antarctic GIA is spatially resolved using a set of global GIA patterns. The patterns are related to deglaciation impulses localized along a grid over Antarctica. GIA associated with four regions outside Antarctica is parametrized by global GIA patterns induced by deglaciation histories. The observations we consider here are satellite gravimetry, satellite altimetry over Antarctica and Greenland, as well as modelled firn thickness changes. Firn thickness changes are also parametrized to account for systematic errors in their modelling. Results from simulation experiments using realistic signals and error covariances support the feasibility of the approach. For example, the spatial RMS error of the estimated Antarctic GIA effect, assuming a 10-year observation period, is 31% and 51%, of the RMS of two alternative global GIA models. The integrated Antarctic GIA error is 8% and 5%, respectively, of the integrated GIA signal of the two models. For these results realistic error covariances incorporated in the parameter estimation process are essential. If error correlations are neglected, the Antarctic GIA RMS error is more than twice as large.Highlights∙ We present a globally consistent inversion approach to co-estimate glacial isostatic adjustment effects together with changes of the ice mass and firn air content in Greenland and Antarctica. ∙ The inversion method utilizes data sets from satellite gravimetry, satellite altimetry, regional climate modelling, and firn modelling together with the full error-covariance information of all input data. ∙ The simulation experiments show that the proposed GIA parametrization in Antarctica can resolve GIA effects unpredicted by geophysical modelling, despite realistic input-data limitations.