The rapid determination of its magnitude soon after a great earthquake is necessary for the issuing of effective tsunami warnings, as demonstrated in the great earthquake off Tohoku district in Japan on March 11, 2011. The earthquake magnitude for the first tsunami warning was underestimated due to magnitude saturation. This paper proposes a method to determine magnitude rapidly from peak velocity and displacement of long-period seismic waves up to 100 seconds at local stations. When waveform data at local stations are available, the magnitude from S-wave peaks is expected to be determined faster than that from only P-wave peaks. It takes about 140 seconds to estimate a magnitude of about 9 for the March 11, 2011, earthquake, which would enable us to issue the first tsunami warning within three minutes after the same type of earthquake.