Prefrontal persistent activity during the delay of spatial working memory tasks is thought to maintain spatial location in memory. A 'bump attractor' computational model can account for this physiology and its relationship to behavior. However, direct experimental evidence linking parameters of prefrontal firing to the memory report in individual trials is lacking, and, to date, no demonstration exists that bump attractor dynamics underlies spatial working memory. We analyzed monkey data and found model-derived predictive relationships between the variability of prefrontal activity in the delay and the fine details of recalled spatial location, as evident in trial-to-trial imprecise oculomotor responses. Our results support a diffusing bump representation for spatial working memory instantiated in persistent prefrontal activity. These findings reinforce persistent activity as a basis for spatial working memory, provide evidence for a continuous prefrontal representation of memorized space and offer experimental support for bump attractor dynamics mediating cognitive tasks in the cortex.