In this paper, we introduce DCOPs with uncertainty (U-DCOPs), a novel generalisation of the canonical DCOP framework where the outcomes of local functions are represented by random variables, and the global objective is to maximise the expectation of an arbitrary utility function (that represents the agents’ risk-profile) applied over the sum of these local functions. We then develop U-GDL, a novel decentralised algorithm derived from Generalised Distributive Law (GDL) that optimally solves U-DCOPs. A key property of U-GDL that we show is necessary for optimality is that it keeps track of multiple non-dominated alternatives, and only discards those that are dominated (i.e. local partial solutions that can never turn into an expected global maximum regardless of the realisation of the random variables). As a direct consequence, we show that applying a standard DCOP algorithm to U-DCOP can result in arbitrarily poor solutions. We empirically evaluate U-GDL to determine its computational overhead and bandwidth requirements compared to a standard DCOP algorithm.