This paper investigates the control of flow networks, where the control objective is to regulate the measured output (e.g. storage levels) towards a desired value. We present a distributed controller that dynamically adjusts the inputs and flows, to achieve output regulation in the presence of unknown constant disturbances, while satisfying given input and flow constraints. Optimal coordination among the controllers minimizing a suitable cost function of the inputs at the nodes, is achieved by exchanging information over a communication network. Exploiting an incremental passivity property, the desired steady state is proven to be globally asymptotically attractive under the closed loop dynamics. Two case studies (a district heating system and a super-conducting DC network) show the effectiveness of the proposed solution. (C) 2019 Elsevier Ltd. All rights reserved.