Joint attention is a core ability of human social cognition which broadly refers to the coordination of attention with both the presence and activity of social partners. In both human and non-human primates, joint attention can be assessed from behaviour; gestures and gaze alternation between the partner and a distal object are standard behavioural manifestations of joint attention. Here we examined the acquisition of joint attention in olive baboons as a function of their individual experience of a human partner's attentional states during training regimes. Eleven olive baboons (Papio anubis) were observed during their training to perform food-requesting gestures, which occurred either by (1) a human facing them (face condition), or (2) by a human positioned in profile who never turned to them (profile condition). We found neither gestures nor gaze alternation were present at the start of the training but rather developed over the training period. Only baboons in the face condition showed an increase in the number of gaze alternations, and their gaze pattern progressively shifted to a coordinated sequence in which gazes and gestures were coordinated in time. In contrast, baboons trained by a human in profile showed significantly less coordination of gazes with gestures but still learned to request food with their gestures. These results suggest that the partner's social attention plays an important role in the acquisition of visual joint attention and, to a lesser extent, in gesture learning in baboons. Interspecific interactions appear to offer rich opportunities to manipulate and thus identify the social contexts in which socio-communicative skills develop.