Recent satellite and hydrographic observations have shown that the rate of freshwater accumulation in the Beaufort Gyre of the Arctic Ocean has accelerated over the past decade. This acceleration has coincided with the dramatic decline observed in Arctic sea ice cover, which is expected to modify the efficiency of momentum transfer into the upper ocean. Here, a simple process model is used to investigate the dynamical response of the Beaufort Gyre to the changing efficiency of momentum transfer, and its link with the enhanced accumulation of freshwater. A linear relationship is found between the annual mean momentum flux and the amount of freshwater accumulated in the Beaufort Gyre. In the model, both the response time scale and the total quantity of freshwater accumulated are determined by a balance between Ekman pumping and an eddy-induced volume flux toward the boundary, highlighting the importance of eddies in the adjustment of the Arctic Ocean to a change in forcing. When the seasonal cycle in the efficiency of momentum transfer is modified (but the annual mean momentum flux is held constant), it has no effect on the accumulation of freshwater, although it does impact the timing and amplitude of the annual cycle in Beaufort Gyre freshwater content. This suggests that the decline in Arctic sea ice cover may have an impact on the magnitude and seasonality of the freshwater export into the North Atlantic.