Along its 650‐km reach, the Peruvian Amazon River comprises anabranching structures, spanning from the confluence of the Marañón and Ucayali Rivers to the Peru–Brazil–Colombia border. Combining remote sensing techniques and field measurements, this research aims to understand the hydrogeomorphology of these anabranching structures. The multitemporal analysis every 5 years over 35 years (1985–2020) reports channel migration rates, erosion/deposition rates, angles of bifurcations and confluences, among other metrics including the number of channels, length, wavelength average, width and sinuosity, as well as the area, shape and number of islands for each structure. Fieldwork also included hydrodynamic measurements along the Peruvian Amazon River to characterize the flow structure and water fluxes. Results showed that the Peruvian Amazon River developed single (stable) and compound (unstable) anabranching structures at a spatial periodicity of about 22.4 km, with an average displacement speed of approximately 74 m/year. Compound anabranching structures were found at the inlet region (near the origin of the Amazon River) and where significant tributaries flow into the main river and water and sediment fluxes impose destabilizing boundary conditions.