Our ability to remember the past is essential for guiding our future behavior. Psychological and neurobiological features of declarative memories are known to transform over time in a process known as systems consolidation. While many theories have sought to explain the time-varying role of hippocampal and neocortical brain areas, the computational principles that govern these transformations remain unclear. Here we propose a theory of systems consolidation in which hippocampal-cortical interactions serve to optimize generalizations that guide future adaptive behavior. We use mathematical analysis of neural network models to characterize fundamental performance tradeoffs in systems consolidation, revealing that memory components should be organized according to their predictability. The theory shows that multiple interacting memory systems can outperform just one, normatively unifying diverse experimental observations and making novel experimental predictions. Our results suggest that the psychological taxonomy and neurobiological organization of declarative memories reflect a system optimized for behaving well in an uncertain future.