We model the geoid anomalies excited during a megathrust earthquake cycle at subduction zones, including the interseismic phase and the contribution from the infinite series of previous earthquakes, within the frame of self-gravitating, spherically symmetric, compressible, viscoelastic Earth models. The fault cuts the whole 50 km lithosphere, dips 20°, and the slip amplitude, together with the length of the fault, are chosen in order to simulate an Mw = 9.0 earthquake, while the viscosity of the 170 km thick asthenosphere ranges from 1017 to 1020 Pa s. On the basis of a new analysis from the Correspondence Principle, we show that the geoid anomaly is characterized by a periodic anomaly due to the elastic and viscous contribution from past earthquakes and to the back-slip of the interseismic phase, and by a smaller static contribution from the steady-state response to the previous infinite earthquake cycles. For asthenospheric viscosities from 1017-1018 to 1019-1020 Pa s, the characteristic relaxation times of the Earth model change from shorter to longer timescales compared to the 400 yr earthquake recurrence time, which dampen the geoid anomaly for the higher asthenospheric viscosities, since the slower relaxation cannot contribute its whole strength within the interseismic cycle. The geoid anomaly pattern is characterized by a global, time-dependent positive upwarping of the geoid topography, involving the whole hanging wall and partially the footwall compared to the sharper elastic contribution, attaining, for a moment magnitude Mw = 9.0, amplitudes as high as 6.6 cm for the lowermost asthenospheric viscosities during the viscoelastic response compared to the elastic maximum of 3.8 cm. The geoid anomaly vanishes due to the back-slip of the interseismic phase, leading to its disappearance at the end of the cycle before the next earthquake. Our results are of importance for understanding the post-seismic and interseismic geoid patterns at subduction zones.