We developed a new tsunami forecasting method using tsunami data observed at offshore ocean bottom tsunami gauges (OBTGs) in order to improve the reliability of the present tsunami warning system based only on the seismic data. In this method, we invert the OBTGs data for the coseismic sea-floor vertical displacement distribution, and calculate tsunami waveforms at coastal sites by using the inverted displacement field as the tsunami source. The inversion and waveform syntheses require only a minute to be accomplished and the method is applicable to real-time warning system. We performed a numerical test assuming the 1896 Sanriku tsunami earthquake. This result indicates that our method can provide estimations of arrival times and wave heights of tsunamis at coastal sites with five minutes and 60 % accuracy, respectively, five minutes before 8 m height tsunami hits the nearest coastal city. We also applied the method to the small amplitude tsunami caused by a local moderate (M6.8) earthquake and succeeded in explaining the arrival times and amplitudes of the tsunami records obtained at coastal tide stations.