Using a network of global navigation satellite systems receivers in New Zealand, located 2,000–3,300 km southwest of Hunga Tonga‐Hunga Ha'apai volcano, we found at least three different kinds of ionospheric disturbances from changes in total electron contents (TEC). Ionospheric signatures of the near‐field acoustic wave propagating ∼0.8 km/s were not clear in New Zealand due possibly to large geometric decay. The first disturbance emerged ∼1 hr after the eruption and traveled toward southwest with a speed of ∼0.6 km/s. This, together with the subsequent disturbance propagating by ∼0.4 km/s, suggests its link to the ahead‐of‐tsunami ionospheric disturbance, excited by the Lamb wave and subsequent tsunamis traveling in the Pacific Ocean. The second disturbance started ∼2 hr after the eruption as tens of waves with periods 10–15 min propagating by ∼0.3 km/s, possibly internal gravity waves (IGW) excited by the passages of the Lamb wave. Such IGW wave trains continued until ∼10 hr after the eruption. The Lamb wave traveled round the earth, and its second and third passages disturbed the ionosphere in New Zealand on the next day as similar IGW wave trains following the Lamb wave. The third disturbance occurred as an enhancement of the harmonic oscillation of TEC with frequency of ∼3.7 mHz, ∼14 hr after the eruption. This might be an atmospheric mode excited by the eruption, but its propagation and sudden activation remain unexplained.