We document two kinds of traveling ionospheric disturbances, namely, CTIDs (Co-tsunami-Traveling-Ionospheric-disturbances) and ATIDs (Ahead-of-Tsunami-Traveling-Ionospheric-disturbances) related to the Tohoku-Oki tsunami of 2011 March 11. They are referred to the disturbances that remain behind and ahead of the principal tsunami wave front, respectively. We first note their presence in a numerical experiment performed using a simulation code coupling the tsunami, atmosphere and ionosphere. This code uses the tsunami wavefield as an input and simulates acoustic-gravity waves (AGWs) in the atmosphere and TIDs, in the form of total electron content (TEC) disturbance, in the ionosphere. The simulated TEC reveals the excitation of CTIDs (at about 2 TECU) and ATIDs (at about 1 TECU), representing up to 5 per cent disturbance over the ambient electron density, and they arise from the dissipation of AGWs in the thermosphere. A novel outcome is that during the tsunami passage between ∼6° and 12° of epicentral distance, strong ATIDs arrive ∼20–60 min ahead of the tsunami wave front covering ∼3°–10° of distance from the tsunami location. Simulation results are compared with the far-field observations using GNSS satellites and confirm that ATIDs are the first detected TEC maximum, occurring 20–60 min ahead of the tsunami arrival. Our simulation also confirms the presence of largest TEC maximum representing CTIDs, 10–20 min after the first tsunami wave. ATIDs reported in this study have characteristics that can be potentially used for the early warning of the tsunami.