Due to tidal interactions in the Earth-Moon system, the spin of the Earth slows down and the Moon drifts away. This recession of the Moon can now be measured with great precision, but it was noticed more than fifty years ago that simple tidal models extrapolated back in time lead to an age of the Moon that is largely incompatible with the geochronological and geochemical evidence. In order to evade this problem, more elaborate models have been proposed, taking into account the oceanic tidal dissipation. However, these models have not been able to fit both the estimated lunar age and the present rate of lunar recession simultaneously. In the present work, we present a physical model that reconciles these two constraints and yields a unique solution for the tidal history. This solution fits the available geological proxies for the history of the Earth-Moon system well and it consolidates the cyclostratigraphic method. Our work extends the lineage of earlier works on the analytical treatment of fluid tides on varying bounded surfaces that is further coupled with solid tidal deformations. This allows us to take into account the time-varying continental configuration on Earth by considering hemispherical and global ocean models. The resulting evolution of the Earth-Moon system involves multiple crossings of resonances in the oceanic dissipation that are associated with significant and rapid variations in the lunar orbital distance, the length of an Earth day and the Earth's obliquity.