  We provide a relation between the geometric framework for $q$-Painlev\'{e}
equations and cluster Poisson varieties by using toric models of rational
surfaces associated with $q$-Painlev\'{e} equations. We introduce the notion of
seeds of $q$-Painlev\'{e} type by the negative semi-definiteness of symmetric
bilinear forms associated with seeds, and classify the mutation equivalence
classes of these seeds. This classification coincides with the classification
of $q$-Painlev\'{e} equations given by Sakai. We realize $q$-Painlev\'{e}
systems as automorphisms on cluster Poisson varieties associated with seeds of
$q$-Painlev\'{e} type.
