Solutions containing guanidinium chloride (GdmCl), or equivalently guanidine hydrochloride (GdnHCl), are commonly used to denature macromolecules such as proteins and DNA in, for example, microfluidics studies of protein unfolding. To design and study such applications, it is necessary to know the diffusion coefficients for GdmCl in the solution. To this end, we use molecular dynamics simulations to calculate the diffusion coefficients of GdmCl in water and in water-ethanol solutions, for which no direct experimental measurements exist. The fully atomistic simulations show that the guandinium cation Gdm (+) diffusion decreases as the concentration of both Gdm (+) and ethanol in the solution increases. The simulations are validated against available literature data, both transformed measured viscosity values and computed diffusion coefficients, and we show that a prudent choice of water model, namely TIP4P-Ew, gives calculated diffusion coefficients in good agreement with the transformed measured viscosity values. The calculated Gdm (+) diffusion behavior is explained as a dynamic mixture of free cation, stacked cation, and ion-paired species in solution, with weighted contributions to Gdm (+) diffusion from the stacked and paired states helping explain measured viscosity data in terms of atom-scale dynamics.