The large tsunami of the 2011 Tohoku-Oki earthquake was clearly recorded by the ocean bottom pressure and GPS wave gauges deployed in and around Japan. We estimated the initial tsunami water height distribution by inversion analysis of the waveforms based on dispersive tsunami simulations. The distribution is characterized by a peak height of 8 m located near the trench and the high-water (>2m) region extending landward with a width of ∼100 km. A series of numerical simulations suggests that a relatively steep peak located near the trench is necessary in order to simultaneously reproduce the dispersive wave at a far-field station and the near-field waveforms. Furthermore, we estimated the coseismic slip distribution at the plate boundary, which indicates that large slip (∼30 m) occurred at a depth of 20 km, which corresponds to a large slip deficit area in the interseismic period. Another slip (∼25 m) occurred at the shallower part (<10 km) during the rupture.