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Meteoroid impacts shape planetary surfaces by forming new craters and alter atmospheric composition. During atmospheric entry and impact on the ground, meteoroids excite transient acoustic and seismic waves. However, new crater formation and the associated impact-induced mechanical waves have yet to be observed jointly beyond Earth. Here we report observations of seismic and acoustic waves from the NASA InSight lander’s seismometer that we link to four meteoroid impact events on Mars observed in spacecraft imagery. We analysed arrival times and polarization of seismic and acoustic waves to estimate impact locations, which were subsequently confirmed by orbital imaging of the associated craters. Crater dimensions and estimates of meteoroid trajectories are consistent with waveform modelling of the recorded seismograms. With identified seismic sources, the seismic waves can be used to constrain the structure of the Martian interior, corroborating previous crustal structure models, and constrain scaling relationships between the distance and amplitude of impact-generated seismic waves on Mars, supporting a link between the seismic moment of impacts and the vertical impactor momentum. Our findings demonstrate the capability of planetary seismology to identify impact-generated seismic sources and constrain both impact processes and planetary interiors.