[en] A systematic method is developed for computing the effects of instanton configurations on binding energies of threshold bound states. Weak coupling and the relevance of the dilute-gas approximation are assumed. The bound-state mass is extracted by studying the asymptotic behavior of the Euclidean two-point function of a current with the quantum numbers of the bound state in question. The formalism is illustrated both for the binding of scalar particles in a (1 + 1) -dimensional Higgs-Abelian model and for quark-antiquark binding in a (3 + 1) -dimensional non-Abelian gauge theory. In the latter case, interactions of exchanged quantum gluons with the background instanton fields are found to induce binding-energy shifts of the same order in the coupling α as direct interaction of quarks with the background fields. The static limit of the leading kernel arising from gluon-instanton interactions is found to depend linearly on the quark-antiquark separation