For a Kac–Moody group G, double Bruhat cells Gu,e (u is a Weyl group element) have positive geometric crystal structures. In Williams (2013), it is shown that there exist birational maps between ‘cluster tori’ XΣ (resp. AΣ) and GAdu,e (resp. Gu,e), and they are extended to regular maps from cluster X (resp. A) -varieties to GAdu,e (resp. Gu,e). The aim of this article is to compute explicit formulae for the induced geometric crystal structures on these cluster tori. As a corollary, the sets of ZT-valued points of these cluster varieties have crystal structures.