Using an approximation scheme within the convective diffusion (two-body Smoluchowski) equation framework, we unveil the shear-driven aggregation mechanism at the origin of structure formation in sheared colloidal systems. The theory, verified against numerics and experiments, explains the induction time followed by explosive (irreversible) rise of viscosity observed in charge-stabilized colloidal and protein systems under steady shear. The Arrhenius-type equation with shear derived here, extending Kramers' theory in the presence of shear, clearly demonstrates the important role of shear drive in activated-rate processes as they are encountered in soft condensed matter.