Under normal cellular conditions, the tumor suppressor protein p53 is kept at a low levels in part due to ubiquitination by MDM2, a process initiated by binding of MDM2 to the intrinsically disordered transactivation domain (TAD) of p53. Although many experimental and simulation studies suggest that disordered domains such as p53 TAD bind their targets nonspecifically before folding to a tightly-associated conformation, the molecular details are unclear. Toward a detailed prediction of binding mechanism, pathways and rates, we have performed large-scale unbiased all-atom simulations of p53-MDM2 binding. Markov State Models (MSMs) constructed from the trajectory data predict p53 TAD binding pathways and on-rates in good agreement with experiment. The MSM reveals that two key bound intermediates, each with a non-native arrangement of hydrophobic residues in the MDM2 binding cleft, control the overall on-rate. Using microscopic rate information from the MSM, we parameterize a simple four-state kinetic model to (1) determine that induced-fit pathways dominate the binding flux over a large range of concentrations, and (2) predict how modulation of residual p53 helicity affects binding, in good agreement with experiment. These results suggest new ways in which microscopic models of bound-state ensembles can be used to understand biological function on a macroscopic scale.