In this paper, we present the first computer simulation of methanol exchange dynamics between the first and second solvation shells around different cations and anions. After water, methanol is the most frequently used solvent for ions. Methanol has different structural and dynamical properties than water, so its ion solvation process is different. To this end, we performed molecular dynamics simulations using polarizable potential models to describe methanol methanol and ion-methanol interactions. In particular, we computed methanol exchange rates by employing the transition state theory, the Impey-Madden-McDonald method, the reactive flux approach, and the Grote-Hynes theory. We observed that methanol exchange occurs at a nanosecond time scale for Na+ and at a picosecond time scale for Cs+, Cl-, and I-. We also observed a trend in which, for like charges, the exchange rate is slower for smaller ions because they are more strongly bound to methanol.