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Abstract Understanding a tsunami source and its impact is vital to assess a tsunami hazard. Thanks to the efforts of the tsunami survey teams, high‐quality tsunami run‐up data exist for contemporary events. Still, it has not been widely used to infer a tsunami source and its impact mainly due to the computational burden of the tsunami forward model. In this study, we propose a TRRF‐INV (Tsunami Run‐up Response Function‐based INVersion) model that can provide probabilistic estimates of a near‐field tsunami source and tsunami run‐up distribution from a small number of run‐up records. We tested the TRRF‐INV model with synthetic tsunami scenarios in northern Chile and applied it to the 2014 Iquique, Chile, tsunami event as a case study. The results demonstrated that the TRRF‐INV model can provide a reasonable tsunami source estimate to first order and estimate tsunami run‐up distribution well. Moreover, the case‐study results agree well with the United States Geological Survey report and the global Centroid Moment Tensor solution. We also analyzed the performance of the TRRF‐INV model depending on the number and the uncertainty of run‐up records. We believe that the TRRF‐INV model has the potential for supporting accurate hazard assessment by (1) providing new insights from tsunami run‐up records into the tsunami source and its impact, (2) using the TRRF‐INV model as a tool to support existing tsunami inversion models, and (3) estimating a tsunami source and its impact for ancient events where no data other than estimated run‐up from sediment deposit data exist.