In this study, we develop stochastic random-field slip models for the 2011 Tohoku earthquake and conduct a rigorous sensitivity analysis of tsunami hazards with respect to the uncertainty of earthquake slip and fault geometry. Synthetic earthquake slip distributions generated from the modified Mai-Beroza method captured key features of inversion-based source representations of the mega-thrust event, which were calibrated against rich geophysical observations of this event. Using original and synthesised earthquake source models (varied for strike, dip, and slip distributions), tsunami simulations were carried out and the resulting variability in tsunami hazard estimates was investigated. The results highlight significant sensitivity of the tsunami wave profiles and inundation heights to the coastal location and the slip characteristics, and indicate that earthquake slip characteristics are a major source of uncertainty in predicting tsunami risks due to future mega-thrust events.