Predicting future events based on previous knowledge about the environment is critical for successful everyday interactions. Here, we ask which brain regions support our ability to predict the future based on implicit knowledge about the past in young and older age. Combining behavioral and fMRI measurements, we test whether training on structured temporal sequences improves the ability to predict upcoming sensory events; we then compare brain regions involved in learning predictive structures between young and older adults. Our behavioral results demonstrate that exposure to temporal sequences without feedback facilitates the ability of young and older adults to predict the orientation of an upcoming stimulus. Our fMRI results provide evidence for the involvement of corticostriatal regions in learning predictive structures in both young and older learners. In particular, we showed learning-dependent fMRI responses for structured sequences in frontoparietal regions and the striatum (putamen) for young adults. However, for older adults, learning-dependent activations were observed mainly in subcortical (putamen, thalamus) regions but were weaker in frontoparietal regions. Significant correlations of learning-dependent behavioral and fMRI changes in these regions suggest a strong link between brain activations and behavioral improvement rather than general overactivation. Thus, our findings suggest that predicting future events based on knowledge of temporal statistics engages brain regions involved in implicit learning in both young and older adults.