Turnover of actin networks in cells requires the fast disassembly of aging actin structures. While ADF/cofilin and Aip1 have been identified as central players, how their activities are modulated by the architecture of the networks remains unknown. Using our ability to reconstitute a diverse array of cellular actin organizations, we found that ADF/cofilin binding and ADF/cofilin-mediated disassembly both depend on actin geometrical organization. ADF/cofilin decorates strongly and stabilizes actin cables, whereas its weaker interaction to Arp2/3 complex networks is correlated with their dismantling and their reorganization into stable architectures. Cooperation of ADF/cofilin with Aip1 is necessary to trigger the full disassembly of all actin filament networks. Additional experiments performed at the single-molecule level indicate that this cooperation is optimal above a threshold of 23 molecules of ADF/cofilin bound as clusters along an actin filament. Our results indicate that although ADF/cofilin is able to dismantle selectively branched networks through severing and debranching, stochastic disassembly of actin filaments by ADF/cofilin and Aip1 represents an efficient alternative pathway for the full disassembly of all actin networks. Our data support a model in which the binding of ADF/cofilin is required to trigger a structural change of the actin filaments, as a prerequisite for their disassembly by Aip1.