The mechanisms by which time-dependent wind stress anomalies at mid-latitudes can force variability in the meridional overturning circulation at low latitudes are explored. It is shown that winds are effective at forcing remote variability in the overturning circulation when forcing periods are near the mid-latitude baroclinic Rossby wave basin-crossing timescale. Remote overturning is required by an imbalance in the mid-latitude mass storage and release resulting from the dependence of the Rossby wave phase speed on latitude. A heuristic theory is developed that predicts the strength and frequency-dependence of the remote overturning well when compared to a two-layer numerical model. The theory indicates that the variable overturning strength, relative to the anomalous Ekman transport, depends primarily on the ratio of the meridional spatial scale of the anomalous wind stress to its latitude. For strongly forced systems, a mean deep western boundary current can also significantly enhance the overturning variability at all latitudes. For sufficiently large thermocline displacements, the deep western boundary current alternates between interior and near-boundary pathways in response to fluctuations in the wind, leading to large anomalies in the volume of North Atlantic Deep Water stored at mid-latitudes and in the downstream deep western boundary current transport.