From a systematic study of the concentration driven diffusion of positive and negative ions across porous 2D membranes of graphene and hexagonal boron nitride (h-BN), we prove their cation selectivity. Using the current−voltage characteristics of graphene and h-BN monolayers separating reservoirs of different salt concentrations, we calculate the reversal potential as a measure of selectivity. We tune the Debye screening length by exchanging the salt concentrations and demonstrate that negative surface charge gives rise to cation selectivity. Surprisingly, h-BN and graphene membranes show similar characteristics, strongly suggesting a common origin of selectivity in aqueous solvents. For the first time, we demonstrate that the cation flux can be increased by using ozone to create additional pores in graphene while maintaining excellent selectivity. We discuss opportunities to exploit our scalable method to use 2D membranes for applications including osmotic power conversion.