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The Queen Charlotte‐Fairweather Fault (QC‐FF) system off the coast of British Columbia and southeast Alaska is a highly active dextral strike‐slip plate boundary that accommodates ∼50 mm/yr of relative motion between the Pacific and North America plates. NineM_W ≥ 6.7 earthquakes have occurred along the QC‐FF system since 1910, including aM_S(G‐R)8.1 event in 1949. Two recent earthquakes, the October 28, 2012 Haida Gwaii (M_W7.8) and January 5, 2013 Craig, Alaska (M_W7.5) events, produced postseismic transient deformation that was recorded in the motions of 25 nearby continuous Global Positioning System (cGPS) stations. Here, we use 5+ yr of cGPS measurements to characterize the underlying mechanisms of postseismic deformation and to constrain the viscosity structure of the upper mantle surrounding the QC‐FF. We construct forward models of viscoelastic deformation driven by coseismic stress changes from these two earthquakes and explore a large set of laterally heterogeneous viscosity structures that incorporate a relatively weak back‐arc domain; we then evaluate each model based on its fit to the postseismic signals in our cGPS data. In determining best‐fit model structures, we additionally incorporate the effects of afterslip following the 2012 event. Our results indicate the occurrence of a combination of temporally decaying afterslip and vigorous viscoelastic relaxation of the mantle asthenosphere. In addition, our best‐fit viscosity structure (transient viscosity of 1.4–2.0 × 10¹⁸ Pa s; steady‐state viscosity of 10¹⁹ Pa s) is consistent with the range of upper mantle viscosities determined in previous studies of glacial isostatic rebound and postseismic deformation.