Previous work has shown that species interacting in an ecosystem and actors transacting in an economic context may have notable similarities in behavior. However, the specific mechanism that may underlie similarities in nature and human systems has not been analyzed. Building on stochastic food-web models, we propose a parsimonious bipartite-cooperation model that reproduces the key features of mutualistic networks - degree distribution, nestedness and modularity -- for both ecological networks and socio-economic networks. Our analysis uses two diverse networks. Mutually-beneficial interactions between plants and their pollinators, and cooperative economic exchanges between designers and their contractors. We find that these mutualistic networks share a key hierarchical ordering of their members, along with an exponential constraint in the number and type of partners they can cooperate with. We use our model to show that slight changes in the interaction constraints can produce either extremely nested or random structures, revealing that these constraints play a key role in the evolution of mutualistic networks. This could also encourage a new systematic approach to study the functional and structural properties of networks. The surprising correspondence across mutualistic networks suggests their broadly representativeness and their potential role in the productive organization of exchange systems, both ecological and social.