The merger of two white dwarfs (WDs) creates a differentially rotating remnant which is unstable to magnetohydrodynamic instabilities. These instabilities can lead to viscous evolution on a time-scale short compared to the thermal evolution of the remnant. We present multidimensional hydrodynamic simulations of the evolution of WD merger remnants under the action of an α-viscosity. We initialize our calculations using the output of eight WD merger simulations from Dan et al., which span a range of mass ratios and total masses. We generically find that the merger remnants evolve towards spherical states on time-scales of hours, even though a significant fraction of the mass is initially rotationally supported. The viscous evolution unbinds only a very small amount of mass . Viscous heating causes some of the systems we study with He WD secondaries to reach conditions of nearly-dynamical burning. It is thus possible that the post-merger viscous phase triggers detonation of the He envelope in some WD mergers, potentially producing a Type Ia supernova via a double-detonation scenario. Our calculations provide the proper initial conditions for studying the long-term thermal evolution of WD merger remnants. This is important for understanding WD mergers as progenitors of Type Ia supernovae, neutron stars, R Coronae Borealis stars and other phenomena.