Anabranching rivers evolve in various geomorphic settings and various river planforms are present within these multi‐channel systems. In some cases, anabranches develop meandering patterns. Such river courses existed in Europe prior to intensive hydro‐technical works carried out during the last 250 years. Proglacial stream valleys, inherited from the last glaciation, provided a suitable environment for the development of anabranching rivers (wide valleys floors with abundant sand deposits). The main objective of the present study is to reconstruct the formation of an anabranching river planform characterized by meandering anabranches. Based on geophysical and geological data obtained from field research and a reconstruction of palaeodischarges, a model of the evolution of an anabranching river formed in a sandy floodplain is proposed. It is demonstrated that such a river system evolves from a meandering to an anabranching planform in periods of high flows that contribute to the formation of crevasse splays. The splay channels evolve then into new meandering flow paths that form ‘second‐order’ crevasses, avulsions and cutoffs. The efficiency of the flow is maintained by the formation of cutoffs and avulsions preventing the development of high sinuosity channels, and redirecting the flow to newly formed channels during maximum flow events. A comparison with other anabranching systems revealed that increased discharges and sediment loads are capable of forming anabranching planforms both in dryland and temperate climate zones. The sediment type available for transport, often inherited from older sedimentary environments, is an important variable determining whether the channel planform is anabranching, with actively migrating channels, or anastomosing, with stable, straight or sinuous branches. Copyright © 2017 John Wiley & Sons, Ltd.