Knowing whether core reward regions carry information about the positions of relevant objects is crucial for adjudicating between choice models. One limitation of previous studies, including our own, is that spatial positions can be consistently differentially associated with rewards, and thus position can be confounded with attention, motor plans, or target identity. We circumvented these problems by using a task in which value- and thus choices-was determined solely by a frequently changing rule, which was randomized relative to spatial position on each trial. We presented offers asynchronously, which allowed us to control for reward expectation, spatial attention, and motor plans in our analyses. We find robust encoding of the spatial position of both offers and choices in two core reward regions, orbitofrontal Area 13 and ventral striatum, as well as in dorsal striatum of macaques. The trial-by-trial correlation in noise in encoding of position was associated with variation in choice, an effect known as choice probability correlation, suggesting that the spatial encoding is associated with choice and is not incidental to it. Spatial information and reward information are not carried by separate sets of neurons, although the two forms of information are temporally dissociable. These results highlight the ubiquity of multiplexed information in association cortex and argue against the idea that these ostensible reward regions serve as part of a pure value domain.