The accurate cleavage of pre‐micro(mi)RNAs by Dicer and mi/siRNA guide strand selection are important steps in forming the RNA‐induced silencing complex (RISC). The role of Dicer binding partner TRBP in these processes remains poorly understood. Here, we solved the solution structure of the two N‐terminal dsRNA binding domains (dsRBDs) of TRBP in complex with a functionally asymmetric siRNA using NMR, EPR, and single‐molecule spectroscopy. We find that siRNA recognition by the dsRBDs is not sequence‐specific but rather depends on the RNA shape. The two dsRBDs can swap their binding sites, giving rise to two equally populated, pseudo‐symmetrical complexes, showing that TRBP is not a primary sensor of siRNA asymmetry. Using our structure to model a Dicer‐TRBP‐siRNA ternary complex, we show that TRBP's dsRBDs and Dicer's RNase III domains bind a canonical 19 base pair siRNA on opposite sides, supporting a mechanism whereby TRBP influences Dicer‐mediated cleavage accuracy by binding the dsRNA region of the pre‐miRNA during Dicer cleavage.