Intrinsically disordered proteins (IDPs) lack stable structures under physiological conditions but often fold into stable structures upon specific binding. These coupled binding and folding processes underlie the organization of cellular regulatory networks, and a mechanistic understanding is thus of fundamental importance. Here, we investigated the synergistic folding of two IDPs, namely, the NCBD domain of transcription coactivator CBP and the p160 steroid receptor coactivator ACTR, using a topology-based model that was carefully calibrated to balance intrinsic folding propensities and intermolecular interactions. As one of the most structured IDPs, NCBD is a plausible candidate that interacts through conformational selection-like mechanisms, where binding is mainly initiated by pre-existing folded-like conformations. Indeed, the simulations demonstrate that, even though binding and folding of both NCBD and ACTR is highly cooperative on the baseline level, the tertiary folding of NCBD is best described by the “extended conformational selection” model that involves multiple stages of selection and induced folding. The simulations further predict that the NCBD/ACTR recognition is mainly initiated by forming a mini folded core that includes the second and third helices of NCBD and ACTR. These predictions are fully consistent with independent physics-based atomistic simulations as well as a recent experimental mapping of the H/D exchange protection factors. The current work thus adds to the limited number of existing mechanistic studies of coupled binding and folding of IDPs, and provides a first direct demonstration of how conformational selection might contribute to efficient recognition of IDPs. Interestingly, even for highly structured IDPs like NCBD, the recognition is initiated by the more disordered C-terminal segment and with substantial contribution from induced folding. Together with existing studies of IDP interaction mechanisms, this argues that induced folding is likely prevalent in IDP–protein interaction, and emphasizes the importance of understanding how IDPs manage to fold efficiently upon (nonspecific) binding. Success of the current study also further supports the notion that, with careful calibration, topology-based models can be effective tools for mechanistic study of IDP interaction and regulation, especially when combined with physics-based atomistic simulations and experiments.