Vanadium redox flow batteries (VRFBs) may be a promising solution for large-scale energy storage applications, but the crossover of any of the redox active species V2+, V3+, VO2+, and VO2+ through the ion exchange membrane will result in self-discharge of the battery. Hence, a molecular level understanding of the states of vanadium cations in the highly acidic environment of a VRFB is needed. We examine the effects of sulfuric and triflic (CF3SO3H) acids on the hydration of vanadium species as they mimic the electrolyte and functional group of perfluorosulfonic acid (PFSA) membranes. Hybrid density functional theory in conjunction with a continuum solvation model was utilized to obtain the local structures of the hydrated vanadium cations in proximity to H2SO4, CF3SO3H, and their conjugate anions. The results indicate that none of these species covalently bond to the vanadium cations. The hydration structure of V3+ is more distorted than that of V2+ in an acidic medium. The oxo-group of VO2+ is protonated by either acid, in contrast to VO2+ which is not protonated. The atomic partial charge of the four oxidation states of vanadium varies from +1.7 to +2.0. These results provide the local solvation structures of vanadium cations in the VRFBs environment that are directly related to the electrolytes stability and diffusion of vanadium ions into the membrane.