Geocoronal H emission data acquired by NASA's Thermosphere Ionosphere Mesosphere Energetics and Dynamics mission are analyzed to quantify the H density distribution over the entire magnetosphere‐ionosphere‐thermosphere region in order to investigate the response of the atmospheric system as a whole to geomagnetic storms. It is shown that at low and middle latitudes the H density averaged over storm times in the thermosphere‐exosphere transition region decreases by ∼30%, while the H density at exospheric altitudes above ∼1–2 RE increases by up to ∼40% relative to quiet times. We postulate that enhanced ion‐neutral charge exchange in the topside ionosphere and inner plasmasphere is the primary driver of the observed H redistribution. Specifically, charge exchange reactions between H atoms and ionospheric/plasmaspheric O+ lead to direct H loss, while those between thermal H and H+ yield kinetically energized H atoms which populate gravitationally bound satellite orbits. The resulting H density enhancements in the outer exosphere would enhance the charge exchange rates in the ring current and the associated energetic neutral atom production. Regardless of the underlying mechanisms, H redistribution should be considered as an important process in the study of storm time atmospheric evolution, and the resultant changes in the geocoronal H emissions potentially could be used to monitor geomagnetic storms.