  The $\Gamma$-colored $d$-complete and $\Gamma$-colored minuscule posets unify
and generalize multiple classes of colored posets introduced by R.A. Proctor,
J.R. Stembridge, and R.M. Green. In previous work, we showed that
$\Gamma$-colored minuscule posets are necessary and sufficient to build from
colored posets certain representations of Kac--Moody algebras that generalize
minuscule representations of semisimple Lie algebras. In this paper we classify
$\Gamma$-colored minuscule posets, which also classifies the corresponding
representations. We show that $\Gamma$-colored minuscule posets are precisely
disjoint unions of colored minuscule posets of Proctor and connected full heaps
of Green. Connected finite $\Gamma$-colored minuscule posets can be realized as
certain posets of coroots in the corresponding finite Lie type.
