This study shows that solutes can impart significant structure to supercritical solutions, resulting in unexpectedly high solution viscosity at pressures close to the critical value. The viscosity passes through a minimum as the pressure is increased, and this is accounted for by a solvation of the solutes leading to a decrease in solute-solute interactions. At high pressure, the solution viscosity is similar to that of the pure solvent as solvent-solvent interactions dominate. The increase in relative viscosity is modeled using a modified Dole-Jones equation, and it is shown that the change in relative viscosity is related to the volume fraction occupied by the solute. A general model is presented for simple solutes whereby the viscosity of a supercritical solution can be calculated from the molecular volume of the solute and the viscosity of the pure fluid. The higher than expected viscosity observed at low pressures is used to explain the variation of reaction rate constant with pressure.