The vast majority of solar cycle predictions focus on predicting the 11-year sunspot cycle, while space weather and geomagnetic activity predictions are largely made for short time scales, from hours up to a month. Here, we aim to predict geomagnetic activity in the solar cycle time scale. We use a 180-year composite of the geomagnetic $aa$ index and fit each $aa$ cycle between two successive sunspot minima with a parameterized asymmetric Gaussian curve. We show that the model reasonably describes the cyclic behavior of $aa$ using only two free parameters. We present how these parameters can be forecasted using past $aa$ values and a recently developed sunspot prediction model. Employing these estimated parameter values, we hindcast each past $aa$ cycle from Solar Cycle 10 onwards and make a prediction for Solar Cycle 25, also estimating the uncertainties using a leave-one-out cross-validation methodology. Each cycle prediction is made at the time of minimum $aa$ starting the respective cycle. For Solar Cycle 25, our prediction gives the $aa$ index maximum of $21 \pm 3\, \mathrm{nT}$ (at the original $aa$ index level) early in the cycle in July 2022, suggesting that Solar Cycle 25, similarly to Solar Cycles 11 and 13, will not have a strong, long-lasting peak of geomagnetic activity in the late declining phase.