Flows of variable viscosity fluids have many industrial applications in fluid mechanics and in engineering such as pump flow for high viscosity fluids. In most cases the fluid viscosity is mainly temperature dependent. Numerical investigation of such flows involves the solution of the Navier-Stokes equations with an extra difficulty arising from the fact that the viscosity is not constant over the flow field. This article presents an analytical solution of the Navier-Stokes equations for the case of laminar flows in rotating systems with variable viscosity fluids, aiming to provide reference solutions for the validation of numerical or empirical prediction models for such flows. In the present method, the analytical solution of the flow field is achieved by expressing the flow variables by using combination of Bessel and exponential functions. It is shown that the proposed solution satisfies the governing equations.