Colloidal gels exhibit time-dependent bulk properties. However, the processes and mechanisms by which aging occurs are poorly understood, which complicates the prediction of macroscopic behavior in these systems. Using a model, thermoreversible, adhesive hard sphere system consisting of octadecyl-coated silica nanoparticles dispersed in tetradecane, rheological aging is quantitatively related to structural aging. By simultaneously measuring the bulk properties and gel microstructure using rheometry and small angle neutron scattering, respectively, we show a one-to-one correspondence between the time-dependent storage modulus and the microstructure, and further, that this correspondence is independent of the gel's thermal and shear history. At the working volume fraction, the gel is homogeneous and, unlike phase-separated gels, aging behavior is not due to heterogeneous coarsening. Instead, the results presented here are consistent with homogeneous, local particle rearrangements as the mechanism of rheological aging. By establishing a quantitative and predictive relationship between the underlying microstructure and bulk mechanical properties, the results of this study may be (1) industrially relevant to products that age on commercially relevant timescales, (2) applicable to other dynamically arrested systems, such as metallic glasses, and (3) valuable in the design of new materials. (C) 2016 The Society of Rheology.