Earthquakes occurring in the Peru-Chile Trench can trigger tsunamis that damage the Peruvian coast. The Directorate of Hydrography and Navigation plans to install three offshore tsunameters in 2023. We propose a tsunami early warning system that uses these tsunameters and targets the Lima Metropolitan Area (LMA), based on the inversion of the initial sea-surface distribution and the superposition of Green's function. Four coastal stations were selected to test the system using historical tsunami events. The forecasts made 15 min after the earthquake had accuracies of 77.0% and 19.4% for the 1966 Huacho and 2001 Camana earthquakes, respectively, whereas the forecasts made 30 min after the earthquake had accuracies of 82.4% and 98.9% for the 1966 and 2001 events, respectively. These results confirmed that the three planned offshore tsunameters will be reliable for making tsunami early warning for the LMA. Moreover, we tested the system using six and ten offshore tsunameters. An increase in the number of offshore tsunameters generally improved the forecast accuracy, but the improvement was not significant. This study is the first to investigate a tsunami early warning algorithm using offshore tsunameters for the Peruvian coast. The results are helpful in mitigating coastal hazards at a reasonable cost.