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Abstract Since the advent of the Space Age, the importance of understanding and forecasting relativistic electron fluxes in the Earth’s radiation belts has been steadily growing due to the threat that such particles pose to satellite electronics. Here, we provide a model of long‐duration periods of high time‐integrated 2‐MeV electron flux deep inside the outer radiation belt, based on the significant correlation obtained in 2001–2017 between time‐integrated electron flux measured by satellites and a measure of the preceding time‐integrated homogenizedaa_Hgeomagnetic index. We show that this correlation is likely due to a stronger cumulative chorus wave‐driven acceleration of relativistic electrons and a stronger cumulative inward radial diffusion of such electrons during periods of higher time‐integrated geomagnetic activity. Return levels of 2‐MeV electron flux are provided based on Extreme Value analysis of time‐integrated geomagnetic activity over 1868–2017, in rough agreement with estimates based on 20‐year data sets of measured flux. A high correlation is also found between our measure of time‐integrated geomagnetic activity averaged over each solar cycle and averaged sunspot numbers, potentially paving the way for forecasts of time‐integrated relativistic electron flux during future solar cycles based on predictions of solar activity.