The probability distribution of far-field tsunami amplitudes is explained in relation to the distribution of seismic moment at subduction zones. Tsunami amplitude distributions at tide gauge stations follow a similar functional form, well described by a tapered Pareto distribution that is parameterized by a power-law exponent and a corner amplitude. Distribution parameters are first established for eight tide gauge stations in the Pacific, using maximum likelihood estimation. A procedure is then developed to reconstruct the tsunami amplitude distribution that consists of four steps: (1) define the distribution of seismic moment at subduction zones; (2) establish a source-station scaling relation from regression analysis; (3) transform the seismic moment distribution to a tsunami amplitude distribution for each subduction zone; and (4) mix the transformed distribution for all subduction zones to an aggregate tsunami amplitude distribution specific to the tide gauge station. The tsunami amplitude distribution is adequately reconstructed for four tide gauge stations using globally constant seismic moment distribution parameters established in previous studies. In comparisons to empirical tsunami amplitude distributions from maximum likelihood estimation, the reconstructed distributions consistently exhibit higher corner amplitude values, implying that in most cases, the empirical catalogs are too short to include the largest amplitudes. Because the reconstructed distribution is based on a catalog of earthquakes that is much larger than the tsunami catalog, it is less susceptible to the effects of record-breaking events and more indicative of the actual distribution of tsunami amplitudes.