In this work, numerical simulations of the atmospheric and ionospheric anomalies are performed for the Tohoku-Oki tsunami (2011 March 11). The Tsunami-Atmosphere-Ionosphere (TAI) coupling mechanism via acoustic gravity waves (AGWs) is explored theoretically using the TAI-coupled model. For the modelled tsunami wave as an input, the coupled model simulates the wind, density and temperature disturbances or anomalies in the atmosphere and electron density/magnetic anomalies in the F region of the ionosphere. Also presented are the GPS-total electron content (TEC) and ground-based magnetometer measurements during the first hour of tsunami and good agreements are found between modelled and observed anomalies. At first, within 6 min from the tsunami origin, the simulated wind anomaly at 250 km altitude and TEC anomaly appear as the dipole-shaped disturbances around the epicentre, then as the concentric circular wave fronts radially moving away from the epicentre with the horizontal velocity ∼800 m s−1 after 12 min followed by the slow moving (horizontal velocity ∼250 m s−1) wave disturbance after 30 min. The detailed vertical-horizontal propagation characteristics suggest that the anomalies appear before and after 30 min are associated with the acoustic and gravity waves, respectively. Similar propagation characteristics are found from the GPS-TEC and magnetic measurements presented here and also reported from recent studies. The modelled magnetic anomaly in the F region ionosphere is found to have similar temporal variations with respect to the epicentre distance as that of the magnetic anomaly registered from the ground-based magnetometers. The high-frequency component ∼10 min of the simulated wind, TEC and magnetic anomalies in the F region develops within 6-7 min after the initiation of the tsunami, suggesting the importance of monitoring the high-frequency atmospheric/ionospheric anomalies for the early warning. These anomalies are found to maximize across the epicentre in the direction opposite to the tsunami propagation suggesting that the large atmospheric/ionospheric disturbances are excited in the region where tsunami does not travel.