Global mean sea level has been rising at a rate of 3.25 ± 0.4 mm yr −1 over 1993–2018. Yet several regions are increasing at a much faster rate, such as the Beaufort Gyre in the Arctic Ocean at a rate of 9.3 ± 7.0 mm yr −1 over 2003–2014. At interannual to decadal time scales, the Beaufort Gyre sea level is controlled by salinity changes due to sea ice melt and wind‐driven lateral Ekman convergence–divergence of freshwater. This study uses recent Greenland discharge and river runoff estimates to isolate and quantify the sea level response to freshwater fluxes variability over the period 1980–2018. It relies on sensitivity experiments based on a global ocean model including sea‐ice and icebergs. These sensitivity experiments only differ by the freshwater fluxes temporal variability of Greenland and global rivers which are either seasonal climatologies or fully time varying, revealing the individual and combined impact of these freshwater sources fluctuations. Fully varying Greenland discharge and river runoff produce an opposite impact on sea level trends over 2005–2018 in the Beaufort Gyre region, the former driving an increase, while the latter, a decrease. Their combined impact leads to a fairly weak sea level trend. The sea level response is primarily driven by salinity variations in the upper 300 m, which are mainly caused by salinity advection involving complex compensations between passive, active, and nonlinear advection. This study shows that including the temporal variability of freshwater fluxes in forced global ocean models results in a better representation of regional sea level change.