Behavioural asymmetries displayed by individuals, such as hand preference and foot preference, tend to be lateralized in the same direction (left or right). This may be because their co-ordination conveys functional benefits for a variety of motor behaviours. To explore the potential functional relationship between key motor asymmetries, we examined whether footedness, handedness, or throwing arm was the strongest predictor of eyedness. Behavioural asymmetries were measured by self-report in 578 left-handed and 612 right-handed individuals. Cluster analysis of the asymmetries revealed four handedness groups: consistent right-handers, left-eyed right-handers, consistent left-handers, and inconsistent left-handers (who were left-handed but right-lateralized for footedness, throwing and eyedness). Supervised machine learning models showed the importance of footedness, in addition to handedness, in determining eyedness. In right-handers, handedness was the best predictor of eyedness, followed closely by footedness, and for left-handers it was footedness. Overall, predictors were more informative in predicting eyedness for individuals with consistent lateral preferences. Implications of the findings in relation to the origins and genetics of handedness and sports training are discussed. Findings are related to fighting theories of handedness and to bipedalism, which evolved after manual dexterity, and which may have led to some humans being right-lateralized for ballistic movements and left-lateralized for hand dexterity.