Solvent exchange facilitates high-density nucleation of sessile nanodroplets or nanobubbles by successively wetting a surface with two solvents of contrasting solubility with respect to a target species. Yet the key physical mechanisms underlying its efficacy have yet to be theoretically explained. We develop a minimal model for solvent exchange, for the prototypical example of water and ethanol as the solvents and nitrogen as the target species. Our calculations show that solvent exchange is mediated by transient solubility gradients that dominate over the intrinsic concentration gradient of nitrogen in the incipient moments after exchange. Solubility gradients advect nitrogen toward the substrate during ethanol-water exchange but away from it in water-ethanol exchange, consistent with the directionality observed in experiments.