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.