We study asymptotic consistency of data-driven distributionally robust optimization with shrinking ambiguity sets. The analysis separates reference-distribution convergence from ambiguity-set shrinkage on a prescribed test-function class. Under compactness and continuity assumptions, this yields uniform convergence of robust objectives, optimal-value convergence, and outer convergence of minimizers. For constrained DRO, the same mechanism gives uniform convergence of robust constraints and Painlev\’e–Kuratowski convergence of feasible regions under a Slater condition. We verify the assumptions for empirical reference measures and generic cost-based optimal-transport ambiguity sets, including the norm-cost case, and extend the framework to MADRO models with uncertain mixture weights.