The Beaufort Gyre (BG) is a large anticyclonic circulation in the Arctic Ocean. Its strength is directly related to the halocline depth, and therefore also to the storage of freshwater. It has recently been proposed that the equilibrium state of the BG is set by the Ice‐Ocean Governor, a negative feedback between surface currents and ice‐ocean stress, rather than a balance between lateral mesoscale eddy fluxes and surface Ekman pumping. However, mesoscale eddies are present in the Arctic Ocean; it is therefore important to extend the Ice‐Ocean Governor theory to include lateral fluxes due to mesoscale eddies. Here, a non‐linear ordinary differential equation is derived that represents the effects of wind stress, the Ice‐Ocean Governor, and eddy fluxes. Equilibrium and time‐varying solutions to this three‐way balance equation are obtained and shown to closely match the output from a hierarchy of numerical simulations, indicating that the analytical model represents the processes controlling BG equilibration. The equilibration timescale derived from this three‐way balance is faster than the eddy equilibration timescale and slower than the Ice‐Ocean Governor equilibration timescales for most values of eddy diffusivity. The sensitivity of the BG equilibrium depth to changes in eddy diffusivity and the presence of the Ice‐Ocean Governor is also explored. These results show that predicting the response of the BG to changing surface forcing and sea ice conditions requires faithfully capturing the three‐way balance between the Ice‐Ocean Governor, wind stress, and eddy fluxes