Although eye movement onset typically precedes hand movement onset when reaching to targets presented in peripheral vision, arm motor commands appear to be issued at around the same time, and possibly in advance, of eye motor commands. A fundamental question, therefore, is whether eye movement initiation is linked or yoked to hand movement. We addressed this issue by having participants reach to targets after adapting to a visuomotor reversal (or 180° rotation) between the position of the unseen hand and the position of a cursor controlled by the hand. We asked whether this reversal, which we expected to increase hand reaction time (HRT), would also increase saccadic reaction time (SRT). As predicted, when moving the cursor to targets under the reversal, HRT increased in all participants. SRT also increased in all but one participant, even though the task for the eyes—shifting gaze to the target—was unaltered by the reversal of hand position feedback. Moreover, the effects of the reversal on SRT and HRT were positively correlated across participants; those who exhibited the greatest increases in HRT also showed the greatest increases in SRT. These results indicate that the mechanisms underlying the initiation of eye and hand movements are linked. In particular, the results suggest that the initiation of an eye movement to a manual target depends, at least in part, on the specification of hand movement.