The construction of fishways for upstream and downstream connectivity is the preferred mitigation measure for hydropower dams and other riverine barriers. Yet empirical evidence for effective design criteria for many species is missing. We therefore assembled a group of international fishway designers and combined their knowledge with available empirical data using a formal expert elicitation protocol and Bayesian networks. The expert elicitation method we use minimizes biases typically associated with such approaches. Demonstrating our application with a case-study on the temperate Southern Hemisphere, we use the resulting probabilistic models to predict the following, given alternative design parameters: (i) the effectiveness of technical fishways for upstream movement of migratory fish; (ii) habitat quality in nature-like bypasses for resident fish; and (iii) rates of mortality during downstream passage of all fish through turbines and spillways. The Fish Passage Network (Fish-Net) predicts that fishways for native species could be near 0% or near 100% efficient depending on their design, suggesting great scope for adequate mitigation. Sensitivity analyses revealed the most important parameters as follows: (i) design of attraction and entrance features of technical fishways for upstream migration; (ii) habitat preferences of resident fish in nature-like bypasses; and (iii) susceptibility of fish to barotrauma and blade strike during turbine passage. Numerical modelling predicted that mortality rates of small-bodied fish (50-100 mm TL) due to blade strike may be higher for Kaplan than Francis turbines. Our findings can be used to support environmentally sustainable decisions in the planning, design and monitoring stages of hydropower development.