When we move through our environment, objects in the visual scene create optic flow patterns on the retina. Even though optic flow is ubiquitous in everyday life, it is not well understood how our eyes naturally respond to it. In small groups of human and non-human primates, optic flow triggers intuitive, uninstructed eye movements to the focus of expansion of the pattern (Knöll, Pillow, & Huk, 2018). Here, we investigate whether such intuitive oculomotor responses to optic flow are generalizable to a larger group of human observers and how eye movements are affected by motion signal strength and task instructions. Observers (N = 43) viewed expanding or contracting optic flow constructed by a cloud of moving dots radiating from or converging toward a focus of expansion that could randomly shift. Results show that 84% of observers tracked the focus of expansion with their eyes without being explicitly instructed to track. Intuitive tracking was tuned to motion signal strength: Saccades landed closer to the focus of expansion, and smooth tracking was more accurate when dot contrast, motion coherence, and translational speed were high. Under explicit tracking instruction, the eyes aligned with the focus of expansion more closely than without instruction. Our results highlight the sensitivity of intuitive eye movements as indicators of visual motion processing in dynamic contexts.