The M7.9 2002 Denali earthquake, Alaska, is one of the largest strike-slip earthquakes ever recorded. The postseismic GPS velocity field around the 300-km-long rupture is characterized by very rapid horizontal velocity up to ~300 mm/yr for the first 0.1 years and slower but still elevated horizontal velocity up to ~100 mm/yr for the succeeding 1.5 years. I find that the spatial and temporal pattern of the displacement field may be explained by a transient mantle rheology. Representing the regional upper mantle as a Burghers body, I infer steady state and transient viscosities of η1 = 2.8 ¿ 1018 Pa s and η2 = 1.0 ¿ 1017 Pa s, respectively, corresponding to material relaxation times of 1.3 and 0.05 years. The lower crustal viscosity is poorly constrained by the considered horizontal velocity field, and the quoted mantle viscosities assume a steady state lower crust viscosity that is 7η1. Systematic bias in predicted versus observed velocity vectors with respect to a fixed North America during the first 3--6 months following the earthquake is reduced when all velocity vectors are referred to a fixed site. This suggests that the post-Denali GPS time series for the first 1.63 years are shaped by a combination of a common mode noise source during the first 3--6 months plus viscoelastic relaxation controlled by a transient mantle rheology.