Far-field tsunami records from the Japanese tide gauge network allow the reexamination of the moment magnitudes (M-w) for the 1906 and 1922 Chilean earthquakes, which to date rely on limited information mainly from seismological observations alone. Tide gauges along the Japanese coast provide extensive records of tsunamis triggered by six great (M-w >8) Chilean earthquakes with instrumentally determined moment magnitudes. These tsunami records are used to explore the dependence of tsunami amplitudes in Japan on the parent earthquake magnitude of Chilean origin. Using the resulting regression parameters together with tide gauge amplitudes measured in Japan we estimate apparent moment magnitudes of M-w 8.0-8.2 and M-w 8.5-8.6 for the 1906 central and 1922 north-central Chile earthquakes. The large discrepancy of the 1906 magnitude estimated from the tsunami observed in Japan as compared with those previously determined from seismic waves (M-s 8.4) suggests a deeper than average source with reduced tsunami excitation. A deep dislocation along the Chilean megathrust would favor uplift of the coast rather than beneath the sea, giving rise to a smaller tsunami and producing effects consistent with those observed in 1906. The 1922 magnitude inferred from far-field tsunami amplitudes appear to better explain the large extent of damage and the destructive tsunami that were locally observed following the earthquake than the lower seismic magnitudes (M-s 8.3) that were likely affected by the well-known saturation effects. Thus, a repeat of the large 1922 earthquake poses seismic and tsunami hazards in a region identified as a mature seismic gap.