Seismological observations provide essential input parameters for numerical tsunami simulations. Here, we present source mechanism parameters, finite-fault source rupture models and numerical tsunami simulation results for the destructive October 28, 2012 Haida Gwaii-Canada (M-w 7.7) and September 16, 2015 Illapel-Chile (M-w 8.3) earthquakes and resulting tsunamis. These two earthquakes were controlled by active tectonic features along the subduction zones that had developed in response to the convergent movements of lithospheric plates. The faulting geometry (strike, dip, and rake angles), focal depth, fault dimensions, average and maximum slip values on the fault planes and seismic moments of the earthquakes are estimated by analyzing teleseismic long-period P- and SH-waves and broadband P-waveforms and using waveform inversion and hybrid back-projection methods. The obtained slip models of the earthquakes reveal heterogeneous slip distributions on fault planes with long source durations (80s and 150s) and low stress drop values (10-15 bars). Numerical simulations of tsunami wave propagation are further performed using the uniform and non-uniform slip models and nonlinear long-wave equations in spherical coordinates. The shape and arrival times of leading tsunami waves are adequately constrained particularly with the heterogeneous slip distribution models. The general characteristics of synthetic tsunami waveforms (e.g., amplitude, shape, arrival time) calculated using the non-uniform slip model, are more consistent with the observed tsunami records than those of a uniform slip model. It is further seen that simulation results using preliminary and fast slip models for both earthquakes give only approximate early tsunami estimates; tsunami wave heights and arrival times to the coasts are mostly not well simulated. The results indicate that tsunami simulations based on finite-fault source slip models likely contribute to the determination of tsunamigenic coastal regions by revealing locations, arrival times, amplitudes, and directions of tsunami waves within a close approximation to observed records off-shore and far from the source region. They provide sufficient information to facilitate tsunami warning and mitigation challenges after the destructive earthquakes. We further suggest that joint inversions of GPS, tsunami, teleseismic and strong ground motion records and higher resolution bathymetry data are needed in order to obtain better correlations between observed and synthetic tsunami data, especially for the later arriving waves.