A method for determining the tsunami magnitude M_t from tsunami run-up heights is developed by using the Abe's (1989) relation which has been employed for estimating run-up heights from earthquake magnitudes. The magnitude M_t is estimated from the relation, M_t=2logH_m+6.6, where H_m is the maximum value of the local-mean run-up height in meters and the logarithmic mean of heights is taken over a distance of about 40km along a coast. Except for unusual events, the moment magnitude can be estimated from M_w=M_t-2C, where C=0 for tsunamis in the fore arc and C=0.2 for tsunamis in the back arc. For 12 large tsunamis that occurred around Japan from 1894 to 1998, M_w estimated from M_t is found to be essentially equivalent to that estimated from seismic waves. The present method is applied to determining M_t for 21 historical tsunamis that occurred around Japan on and after the 15th century. There are 13 large tsunamis with M_t=8 or over for the period from 1498 to 1893.