Due to delays in visuo-motor processing, eye movements directed toward moving targets must integrate both target position and velocity to be accurate. It is unknown where and how target velocity information is incorporated into the planning of rapid (saccadic) eye movements. We recorded the activity of neurons in frontal eye fields (FEF) while monkeys made saccades to stationary and moving targets. A substantial fraction of FEF neurons were found to encode not only the initial position of a moving target, but the metrics (amplitude and direction) of the saccade needed to intercept the target. Many neurons also encoded target velocity in a nearly linear manner. The quasi-linear dependence of firing rate on target velocity means that the neuronal response can be directly read-out to compute the future position of a target moving with constant velocity. This is demonstrated using a quantitative model in which saccade amplitude is encoded in the population response of neurons tuned to retinal target position and modulated by target velocity.