It has been known for many years that a spreading liquid droplet can be appreciably slowed on a soft, viscoelastic substrate by the appearance of a "wetting ridge" or protuberance of the solid near the triple phase contact line because of capillary forces. Viscoelastic dissipation in the solid surface can outweigh that of liquid viscosity and, therefore, dominate wetting dynamics. In this paper, we show that a short, rapid spreading stage exists after initial contact. The requisite balance determining the speed of motion is between capillary forces and inertial effects. As spreading proceeds, however, inertia lessens and the lower spreading speed allow for viscoelastic effects in the solid to increase. The transition between early inertial and viscoelastic regimes is studied with high-speed photography and explained by a simple theory.