Ion atmospheres play a critical role in modulating the interactions between charged components in solutions. However, a detailed description of the nature of ion atmospheres remains elusive. Here, we use Kirkwood-Buff theory, an exact theory of solution mixtures, together with a series of local and bulk electroneutrality constraints to provide relationships between all the net ion-ion distributions in bulk electrolyte mixtures. The validity of the underlying relationships is then confirmed using classical explicit solvent molecular simulations of a range of electrolyte mixtures. Further analysis indicates the ion distributions can be separated into two contributions, one resulting in charge neutralization, for which each ion contributes in proportion to its ionic strength, and the other accounting for all the solution thermodynamics. The relationships hold for atomic and molecular ions of any size and valency regardless of ionic strength, temperature, or pressure, in any solvent system.