During behavior, the oculomotor system is tasked with selecting objects from an ever-changing visual field and guiding eye movements to these locations. The attentional priority given to visual targets during selection can be strongly influenced by external stimulus properties or internal goals based on previous experience. Although these exogenous and endogenous drivers of selection are known to operate across partially overlapping timescales, the form of their interaction over time remains poorly understood. Using a novel choice task that simultaneously manipulates stimulus-and goal-driven attention, we demonstrate that exogenous and endogenous attentional biases change linearly as a function of time after stimulus onset and have an additive influence on the visual selection process in rhesus macaques (Macaca mulatta). We present a family of computational models that quantify this interaction over time and detail the history dependence of both processes. The computational models reveal the existence of a critical 140 -180 ms attentional "switching" time, when stimulus- and goal-driven processes simultaneously favor competing visual targets. These results suggest that the brain uses a linear sum of attentional biases to guide visual selection.