We have retrieved the latitudinal and vertical structures of the 11 year solar cycle modulation on ionospheric electron density using 14 years of satellite-based radio occultation measurements utilizing the Global Positioning System. The densities at the crests of the equatorial ionization anomaly (EIA) in the subtropics near 300 km in 2003 and 2014 (high solar activity with solar 10.7 cm flux, F10.7 ≈ 140 solar flux unit (sfu)) were 3 times higher than that in 2009 (low solar activity F10.7 ≈ 70 sfu). The higher density is attributed to the elevated solar extreme ultraviolet and geomagnetic activity during high solar activity periods. The location of the EIA crests moved ~50 km upward and ~10° poleward, because of the enhanced E × B force. The EIA in the northern hemisphere was more pronounced than that in the southern hemisphere. This interhemispheric asymmetry is consistent with the effect of enhanced transequatorial neutral wind. The above observations were reproduced qualitatively by the two benchmark runs of the Thermosphere-Ionosphere-Electrodynamics General Circulation Model. In addition, we have studied the impact of the 11 year solar cycle on the 27 day solar cycle response of the ionospheric electron density. Beside the expected modulation on the amplitude of the 27 day solar variation due to the 11 year solar cycle, we find that the altitude of the maximal 27 day solar response is unexpectedly ~50 km higher than that of the 11 year solar response. This is the first time that a vertical dependence of the solar responses on different time scales is reported.