We study the η and η′ distribution amplitudes (DAs) in the context of a nonlocal SU(3)_L ⊗ SU(3)_R chiral quark model. The corresponding Lagrangian allows us to reproduce the phenomenological values of pseudoscalar meson masses and decay constants, as well as the momentum dependence of the quark propagator arising from lattice calculations. It is found that the obtained DAs have two symmetric maxima, which arise from new contributions generated by the nonlocal character of the interactions. These DAs are then applied to the calculation of the η-γ and η′-γ transition form factors. Implications of our results regarding higher twist corrections and/or contributions to the transition form factors originated by gluon-gluon components in the η and η′ mesons are discussed.