An application of the original numerical inversion technique to modeling the tsunami sources of the 16 September 2015 Chile tsunami is presented. The problem of recovering a tsunami source from remote measurements of the incoming wave in the deep-water tsunameters is considered as an inverse problem of mathematical physics in the class of ill-posed problems. This approach is based on the least squares and the truncated singular value decomposition techniques. As is done in the inverse seismic problem, the numerical solutions obtained by mathematical methods become unstable due to the presence of noise in real data. The method proposed suppresses the negative effect of the ill-posedness of the problem determining the inevitable instability of the numerical solution. Implementation of the methodology proposed to the 16 September 2015 Chile tsunami has successfully produced the tsunami source model. The tsunami source recovered by the method proposed can find practical applications both as an initial condition for various optimization approaches and for computer-aided calculation of the tsunami wave propagation.