Recent observations have revealed large F-region electron density perturbations (~100%) and total electron content (TEC) perturbations (~30%) that appear to be correlated with tsunamis. The characteristic speed and horizontal wavelength of the disturbances are ~200 m/s and ~400 km. We describe numerical simulations using our spectral full-wave model (SFWM) of the upward propagation of a spectrum of gravity waves forced by a tsunami, and the interaction of these waves with the F-region ionosphere. The SFWM describes the propagation of linear, steady-state acoustic-gravity waves in a nonisothermal atmosphere with the inclusion of eddy and molecular diffusion of heat and momentum, ion drag, Coriolis force, and height-dependent mean winds. The tsunami is modeled as a deformation of our model lower boundary traveling at the shallow water wave speed of 200 m/s with a maximum vertical displacement of 50 cm and described by a modified Airy function in the horizontal direction. The derived vertical velocity spectrum at the surface describes the forcing at the lower boundary of the SFWM. A steady-state 1-D ionospheric perturbation model is used to calculate the electron density and TEC perturbations. The molecular diffusion strongly damps the waves in the topside (>300-km altitude) ionosphere. In spite of this, the F-region response is large, with vertical displacements of ~2 to 5 km and electron density perturbations of ~100%. Mean winds have a profound effect on the ability of the waves to propagate into the F-region ionosphere.