Large tsunamis occur infrequently but have the capacity to cause enormous numbers of casualties, damage to the built environment and critical infrastructure, and economic losses. A sound understanding of tsunami hazard is required to underpin management of these risks, and while tsunami hazard assessments are typically conducted at regional or local scales, globally consistent assessments are required to support international disaster risk reduction efforts, and can serve as a reference for local and regional studies. This study presents a global-scale probabilistic tsunami hazard assessment (PTHA), extending previous global-scale assessments based largely on scenario analysis. Only earthquake sources are considered, as they represent about 80% of the recorded damaging tsunami events. Globally extensive estimates of tsunami run-up height are derived at various exceedance rates, and the associated uncertainties are quantified. Epistemic uncertainties in the exceedance rates of large earthquakes often lead to large uncertainties in tsunami run-up. Deviations between modelled tsunami run-up and event observations are quantified, and found to be larger than suggested in previous studies. Accounting for these deviations in PTHA is important, as it leads to a pronounced increase in predicted tsunami run-up for a given exceedance rate.