The a–posteriori identifiability of the Maxwell Slip model of hysteresis is addressed. The necessary and sufficient conditions that guarantee that the available data are informative enough are provided. An Output Error type estimator is subsequently postulated and its consistency is established. It is specifically shown that the estimates converge in probability to their actual counterparts under easily verifiable conditions on the Maxwell Slip model structure, the excitation, and mild assumptions on the additive measurement noise. The analytical results are verified through Monte Carlo simulations.