The solution of a problem left unresolved in the evening can sometimes pop into mind as a sudden insight after a night of sleep in the following morning. Although favorable effects of sleep on insightful behavior have been experimentally confirmed, the neural mechanisms determining this delayed insight remain unknown. Here, using fMRI, we characterize the neural precursors of delayed insight in the number reduction task (NRT), in which a hidden task structure can be learned implicitly, but can also be recognized explicitly in an insightful process, allowing immediate qualitative improvement in task performance. Normal volunteers practiced the NRT during two fMRI sessions (training and retest), taking place 12 hours apart after a night of sleep. After this delay, half of the subjects gained insight into the hidden task structure ("solvers," S), whereas the other half did not ("nonsolvers," NS). Already at training, solvers and nonsolvers differed in their cerebral responses associated with implicit learning. In future solvers, responses were observed in the superior frontal sulcus, posterior parietal cortex, and the insula, three areas mediating controlled processes and supporting early learning and novice performance. In contrast, implicit learning was related to significant responses in the hippocampus in nonsolvers. Moreover, the hippocampus was functionally coupled with the basal ganglia in nonsolvers and with the superior frontal sulcus in solvers, thus potentially biasing participants' strategy towards implicit or controlled processes of memory encoding, respectively. Furthermore, in solvers but not in nonsolvers, response patterns were further transformed overnight, with enhanced responses in ventral medial prefrontal cortex, an area previously implicated in the consolidation of declarative memory. During retest in solvers, before they gain insight into the hidden rule, significant responses were observed in the same medial prefrontal area. After insight, a distributed set of parietal and frontal areas is recruited among which information concerning the hidden rule can be shared in a so-called global workspace.