Abstract. In this paper we characterize the so called uniformly rectifiable sets of David and Semmes in terms of the Wasserstein distance W 2 from optimal mass transport. To obtain this result, we first prove a localization theorem for the distance W 2 which asserts that if µ and ν are probability measures in R n , ϕ is a radial bump function smooth enough so that ∫ ϕ dµ ≳ 1, and µ has a density bounded from above and from below on supp(ϕ), then W 2 (ϕµ, aϕν) ≤ c W 2 (µ, ν), where a = ∫ ϕ dµ ∫ ϕ dν.