We propose a new probabilistic scheme for the automatic recognition of underwater acoustic signals generated by teleseismic P-waves recorded by hydrophones in the ocean. The recognition of a given signal is based on the relative distribution of its power among different frequency bands. The signal's power distribution is compared with a statistical model developed by analyzing relative power distributions of many signals of the same origin and a numerical criterion is calculated, which can serve as a measure of the probability for the signal to belong to the statistical model. Our recognition scheme was applied to 6-month-long continuous records of seven ocean bottom hydrophones (OBH) deployed in the Ligurian Sea. A maximum of 94% of all detectable teleseismic P-waves recorded during the deployment of the OBHs were recognized correctly with no false recognitions. The proposed recognition method will be implemented in autonomous underwater robots dedicated to detect and transmit acoustic signals generated by teleseismic P-waves.