Memory encoding for important information can be enhanced both by reward anticipation and by intentional strategies. These effects are hypothesized to depend on distinct neural mechanisms, yet prior work has provided only limited evidence for their separability. We aimed to determine whether reward-driven and strategic mechanisms for prioritizing important information are separable, even if they may also interact. We examined the joint operation of both mechanisms using fMRI measures of brain activity. Participants learned abstract visual images in a value-directed recognition paradigm. On each trial, two novel images were presented simultaneously in different screen quadrants, one arbitrarily designated as high point value and one as low value. Immediately after each block of 16 study trials, the corresponding point rewards could be obtained in a test of item recognition and spatial location memory. During encoding trials leading to successful subsequent memory, especially of high-value images, increased activity was observed in dorsal frontoparietal and lateral occipitotemporal cortex. Furthermore, activity in a network associated with reward was higher during encoding when any image, of high or low value, was subsequently remembered. Functional connectivity between right medial temporal lobe and right ventral tegmental area, measured via psychophysiological interaction, was also greater during successful encoding regardless of value. Strategic control of memory, as indexed by successful prioritization of the high-value image, affected activity in dorsal posterior parietal cortex as well as connectivity between this area and right lateral temporal cortex. These results demonstrate that memory can be strengthened by separate neurocognitive mechanisms for strategic control versus reward-based enhancement of processing.