Antarctic Bottom Water (AABW) formation and transport constitute a key component of the global ocean circulation. Direct observations suggest that AABW volumes and transport rates may be decreasing, but these observations are too temporally or spatially sparse to determine the cause. To address this problem, we develop a new method to reconstruct AABW transport variability using data from the GRACE (Gravity Recovery and Climate Experiment) satellite mission. We use an ocean general circulation model to investigate the relationship between ocean bottom pressure and AABW: we calculate both of these quantities in the model, and link them using a regularised linear regression. Our reconstruction from modelled ocean bottom pressure can capture 65-90% of modelled AABW transport variability, depending on the ocean basin. When realistic observational uncertainty values are added to the modelled ocean bottom pressure, the reconstruction can still capture 30-80% of AABW transport variability. Using the same regression values, the reconstruction skill is within the same range in a second, independent, general circulation model. We conclude that our reconstruction method is not unique to the model in which it was developed and can be applied to GRACE satellite observations of ocean bottom pressure. These advances allow us to create the first global reconstruction of AABW transport variability over the satellite era. Our reconstruction provides information on the interannual variability of AABW transport, but more accurate observations are needed to discern AABW transport trends.