Manual gestures and speech recruit a common neural network, involving Broca area in the left hemisphere. Evolutionary questions about this language organization led to a renewed attention for comparative research on gestural communication in our closer primate relatives and its potential language-like features. Here, using in vivo anatomical MRI in 80 baboons, we found that communicative gesturing’s lateralisation – but not handedness for manipulation - is related to Broca homologue’s marker in monkeys, namely contralateral depth hemispheric asymmetry of the ventral portion of the inferior arcuate sulcus. This finding provides strong support for the gestural evolutionary continuities with language-related frontal specialization, dating back not only to Homo sapiens evolution, but rather to a much older common ancestor shared with old-world monkeys, 25-35 million years ago.