Objectives In many primates, the greater proportion of climbing and suspensory behaviors in the juvenile repertoire likely necessitates good grasping capacities. Here, we tested whether very young individuals show near-maximal levels of grasping strength, and whether such an early onset of grasping performance could be explained by ontogenetic variability in the morphology of the limbs in baboons. Material and methods We quantified a performance trait, hand pull strength, at the juvenile and adult stages in a cross-sectional sample of 15 olive baboons (Papio anubis). We also quantified bone dimensions (i.e., lengths, widths, and heights) of the fore- (n = 25) and hind limb (n = 21) elements based on osteological collections covering the whole development of olive baboons. Results One-year old individuals demonstrated very high pull strengths (i.e., 200% of the adult performance, relative to body mass), that are consistent with relatively wider phalanges and digit joints in juveniles. The mature proportions and shape of the forelimb elements appeared only at full adulthood (i.e., ≥4.5 years), whereas the mature hind limb proportions and shape were observed much earlier during development. Discussion These changes in limb performance and morphology across ontogeny may be explained with regard to behavioral transitions that olive baboons experience during their development. Our findings highlight the effect of infant clinging to mother, an often-neglected feature when discussing the origins of grasping in primates. The differences in growth patterns, we found between the forelimb and the hind limb further illustrate their different functional roles, having likely evolved under different ecological pressures (manipulation and locomotion, respectively).