We introduce a general hybrid approach for determining the structures of supramolecular assemblies. Cryo-electron microscopy (cryo-EM) data define the overall envelope of the assembly and rigid-body orientation of the subunits while solid-state nuclear magnetic resonance (ssNMR) chemical shifts and distance constraints define the local secondary structure, protein fold and inter-subunit interactions. Finally, Rosetta structure calculations provide a general framework to integrate the different sources of structural information. Combining a 7.7-Å cryo-EM density map and 996 ssNMR distance constraints, the structure of the type-III secretion system needle of Shigella flexneri is determined to a precision of 0.4 Å. The calculated structures are cross-validated using an independent data set of 691 ssNMR constraints and scanning transmission electron microscopy measurements. The hybrid model resolves the conformation of the non-conserved N terminus, which occupies a protrusion in the cryo-EM density, and reveals conserved pore residues forming a continuous pattern of electrostatic interactions, thereby suggesting a mechanism for effector protein translocation.