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Acting in the natural world requires not only deciding among multiple options but also converting decisions into motor commands. The link between the dynamics of decision formation and the kinematics of response movement remains poorly understood. Here we investigate how the accumulation of decision evidence shapes response trajectories in a task where freely-moving rats combine prior expectations and acoustic information to select between two possible options. Rats' trajectories extracted from automatic video analysis showed that the vigor of rats' movements was initially set by the prior expectations. Rats incorporated the stimulus information after the response onset by speeding their response if the stimulus supported their choice, slowing it otherwise, or even reversing their initial trajectories to head to the alternative port when the stimulus clearly contradicted the initial choice. A remarkably similar behavior was found in humans performing an analogous task under time pressure. We encapsulated this behavior in a computational model that describes the mapping between the dynamics of evidence accumulation and the full response trajectory. The model replicates the subjects choices, response trajectories and explains the conditions yielding trajectory reversals. Together, our results show the tight and graded relationship between the evidence accumulated during perceptual decisions and the kinematics of the response trajectories described by rats and humans to execute their choices.