This study presents a fully decentralised robust optimisation (RO) approach for multi‐area economic dispatch (MA‐ED) in the presence of wind power uncertainty. Unlike traditional algorithms, the authors formulate this MA‐ED problem as dynamic programming problem, and decompose the centralised robust MA‐ED problem into a series of sub‐problems based on approximate dynamic programming algorithm. The value functions are proposed for each area to iteratively estimate the impacts of its dispatches on the dispatches of other areas which make decisions subsequently. The proposed algorithm does not require a central operator but only needs to exchange a small amount of information among neighbouring areas to achieve fully decentralised decision‐making. It is practical in cases where the centralised operator cannot be implemented considering the dispatch independence and the detailed data of one area is unavailable considering the privacy. Additionally, the accuracy, adaptability and computational efficiency of the proposed algorithm are illustrated using numerical simulations on two test systems and an actual power system.