Bayesian optimal experimental design (OED) provides a principled framework for choosing experimental settings that maximize the informativeness of collected data. Traditional Bayesian OED has relied heavily on the expected information gain (EIG), based on Kullback–Leibler divergence, or variance-reduction criteria such as A-optimality. In this talk, we introduce a new design criterion grounded in optimal transport: the expected Wasserstein distance between prior and posterior distributions. This criterion inherits the fully Bayesian character of EIG while offering geometric and stability advantages. For Gaussian regression models, the Wasserstein-2 criterion yields explicit formulas akin to classical optimality measures, making it computationally tractable. A central contribution of our work is a stability analysis of the Wasserstein-1 criterion; this demonstrates robustness under perturbations of the prior and likelihood and enables rigorous error control when empirical priors are used.