The Tonga volcano eruption at 04:14:45 UT on 2022-01-15 released enormous amounts of energy into the atmosphere, triggering very significant geophysical variations not only in the immediate proximity of the epicenter but also globally across the whole atmosphere. This study provides a global picture of ionospheric disturbances over an extended period for at least four days. We find traveling ionospheric disturbances (TIDs) radially outbound and inbound along entire Great-Circle loci at primary speeds of ~300-350 m/s (depending on the propagation direction) and 500-1000 km horizontal wavelength for front shocks, going around the globe for three times, passing six times over the continental US in 100 hours since the eruption. TIDs following the shock fronts developed for ~8 hours with 10-30 min predominant periods in near- and far- fields. TID global propagation is consistent with the effect of Lamb waves which travel at the speed of sound. Although these oscillations are often confined to the troposphere, Lamb wave energy is known to leak into the thermosphere through channels of atmospheric resonance at acoustic and gravity wave frequencies, carrying substantial wave amplitudes at high altitudes. Prevailing Lamb waves have been reported in the literature as atmospheric responses to the gigantic Krakatoa eruption in 1883 and other geohazards. This study provides substantial first evidence of their long-duration imprints up in the global ionosphere. This study was enabled by ionospheric measurements from 5,000+ world-wide Global Navigation Satellite System (GNSS) ground receivers, demonstrating the broad implication of the ionosphere measurement as a sensitive detector for atmospheric waves and geophysical disturbances.