Gesturing is a widespread phenomenon in the animal kingdom, as well as an important facet of human language. As such, studying the communicative gestures of our close phylogenetic relatives is essential to better understand its evolution. While recent studies have shown that ape gestural communication shares some properties with human language, very little is known about the properties of gestural communication in monkeys. The aims of this study were to establish the first quantitative repertoire of gestural communication in a species of old-world monkeys, the olive baboon Papio anubis, and to determine its properties in terms of variability, flexibility, and intentionality. Gestural communication was continuously recorded on 47 captive olive baboons over 1 year. Their gestural repertoire was composed of 67 visual, tactile, and audible gestures, which were used flexibly across different contexts, indicating means–ends dissociation. We found that the use of gestures was variable across individuals and ages, notably with repertoire size decreasing with age. Baboons used their gestures intentionally; gesturers looked at the recipient, waited for a response, and took into account the attentional state of their recipient. Particularly, they actively adjusted the modality of their gesture to the recipient’s visual attention, using more visual gestures when the recipient was attending and more tactile gestures when the recipient was not. Thus, the gestural communicative system of olive baboons possesses properties which are similar to the ones of apes and to human language. These intentional features of gestural communication, that may constitute a prerequisite of language evolution, may have been present in the common ancestor of baboons and humans, around 30–40 million years ago.